) Study cited that the calcium levels in men and women ages 70 years or older are summarized that sample size of 55 men with mean 785 and standard deviation 489 and sample size of 40 women with mean 670 and standard deviation of 419, what is the probability of obtaining a difference between sample means of 110 mg or more?
Answer:
0.5188 = 51.88% probability of obtaining a difference between sample means of 110 mg or more
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution, the central limit theorem and difference between normal variables.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction of normal sample means:
When we subtract two distribution of the sample means, which are normal, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of standard errors squared.
Sample size of 55 men with mean 785 and standard deviation 489
This means that:
[tex]\mu_A = 785[/tex]
[tex]s_A = \frac{489}{\sqrt{55}} = 65.9367[/tex]
Sample size of 40 women with mean 670 and standard deviation of 419
This means that:
[tex]\mu_B = 670[/tex]
[tex]s_B = \frac{419}{\sqrt{40}} = 66.2497[/tex]
Difference between sample means:
The mean and the standard deviation are, respectively:
[tex]\mu = \mu_A - \mu_B = 785 - 670 = 115[/tex]
[tex]\sigma = \sqrt{s_A^2+s_B^2} = \sqrt{65.9367^2+66.2497^2} = 93.47[/tex]
What is the probability of obtaining a difference between sample means of 110 mg or more?
This is 1 subtracted by the pvalue of Z when X = 110. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{110 - 115}{93.47}[/tex]
[tex]Z = -0.053[/tex]
[tex]Z = -0.053[/tex] has a pvalue of 0.4812.
1 - 0.4812 = 0.5188
0.5188 = 51.88% probability of obtaining a difference between sample means of 110 mg or more
A density graph for all of the possible temperatures from 60 degrees to 160 degrees can be used to find which of the following?
A.The probability of a temperature from 30 degrees to 120 degrees
B.The probability of a temperature from 90 degrees to 180 degrees
C.The probability of a temperature from 30 degrees to 90 degrees
D.The probability of a temperature from 90 degrees to 120 degrees
Answer: 90 degrees to 120
Step-by-step explanation:
The probability of a temperature from 90 degrees to 120 degrees.
What is Probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
Experiment: A trial or an operation conducted to produce an outcome is called an experiment.
Sample Space: All the possible outcomes of an experiment together constitute a sample space. For example, the sample space of tossing a coin is head and tail.
Favorable Outcome: An event that has produced the desired result or expected event is called a favorable outcome. For example, when we roll two dice, the possible/favorable outcomes of getting the sum of numbers on the two dice as 4 are (1,3), (2,2), and (3,1).
Trial: A trial denotes doing a random experiment.
Given:
Temperatures from 60 degrees to 160 degrees.
As, per the situation the probability will lie between 60 degree to 160 degree.
Hence, The probability of a temperature from 90 degrees to 120 degrees.
Learn more about probability here:
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Plz help me well mark brainliest if you are correct!!
Answer:
A four one quarter
Step-by-step explanation:
6³ . 2⁶ |Which expressions are equal to 2³ ? |126 23 . 33 26. 33 123
Answer:
26 and 126
Step-by-step explanation:
hope this helps:))))
Answer:
Step-by-step explanation:
vbh th78g its a
The numbers of licensed drivers in four samples taken from a population of
students are shown in the table below. Which of the following choices is most
likely closest to the percentage of students in the population who are
licensed drivers?
Sample Size Number of Licensed Drivers
25
7
50
12
75
15
100
16
O A. 16%
O B. 20%
ОООО
C. 24%
O D. 28%
Answer:
The answer is 16% I just took the test
Step-by-step explanation:
look at pic 10 pts will mark brainilest
Answer:
A- point A
Step-by-step explanation:
Absolute value doesnt care about the sign so a negative is a positive.
PLease Brainliest
Mohamed spent $40 buying three pizzas do you order the wings roommates. Each pizza cost twice as much as the wings +1 dollar. What does one order of wings cost
Answer:
26
Step-by-step explanation:
A coach of a baseball team orders hats for the players on his team. Each hat costs $9.95. The shipping charge for the entire order is $5.00. The total cost of the coach's order is less than $125.00. What inequality can be used to determine the greatest number of hats, h, the coach orders
Answer:
H ≤ 125
Step-by-step explanation:
The coach can order 12 hats
what fraction belongs in the box?
l_i_i_i_i_l_i_i_i_i_l_i_i_i_i_l_i_i_i_i_l_i_i_i_i_l___
0 1 2 3 4
*box
Your weekly allowance is $15. You spent 30% How much did you spend?
Answer:
You would have spent $4.50
Step-by-step explanation: Divide 100 by 30 and multiply to 15. So it will look like: 30/100*15= $4.50. I hope this helps
quadratic formula to find the zeros
b^2-4b+4=0
Answer:
Step-by-step explanation:
Remark
I don't think you need the quadratic formula for this equation. It just factors into (b - 2)(b - 2), but I'll do it because you requested it.
Formula
[tex]\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac } }{2a}[/tex]
Givens
a = 1
b = - 4
c = 4
Solution
x = - - 4 +/- sqrt((-4^2) - 4*1*4)
====================
2*1
x = 4 +/- sqrt (16 - 16)
==========
2
x = 4/2
x = 2
There are 2 roots but both of them are the same. Some teachers say there is only 1 root. I'm in that group.
Ambrosone et al. (2004) conducted an observational study to explore whether broccoli consumption reduces the risk of developing breast cancer in premenopausal women. They report a p-value of 0.058. PROPOSITION ONE: The results suggest a statistically significant association between broccoli consumption and reduced risk of breast cancer at the 5% significance level; PROPOSITION TWO: The results prove the null hypothesis at the 5% significance level.
a. PROPOSITION ONE is true and PROPOSITION TWO is true
b. PROPOSITION ONE is true and PROPOSITION TWO is false
c. PROPOSITION ONE is false and PROPOSITION TWO is true
d. PROPOSITION ONE is false and PROPOSITION TWO is false
e. None of the above
Answer:
c. PROPOSITION ONE is false and PROPOSITION TWO is true
Step-by-step explanation:
In this question, we have that:
pvalue of 0.058
Significance level of 0.05
The pvalue is larger than the significance level, which means that there is no statistically significant association(Propostion One is false), and the null hypothesis is not rejected, that is, it is proved, so Proposition Two is true.
This means that the correct answer is given by option C.
Guys please tell me the answer
Answer:
from 10 - 15 bikes
Step-by-step explanation:
there's 20 points for both problems if you could please solve this
Solve the exponential equation for x
3^7x+4=(1/27)^x-3
Answer:
The solution is [tex]x = \frac{1}{2}[/tex]
Step-by-step explanation:
To solve this exponential equation, we must write both sides as powers of 3.
The equation given is:
[tex]3^{7x + 4} = (\frac{1}{27})^{x-3}[/tex]
Since [tex]3^3 = 27[/tex], we have that [tex]3^{-3} = \frac{1}{3^3} = \frac{1}{27}[/tex], so[tex]\frac{1}{27} = 3^{-3}[/tex]
Then
[tex]3^{7x + 4} = (\frac{1}{27})^{x-3}[/tex]
[tex]3^{7x + 4} = (3^{-3})^{x-3}[/tex]
[tex]3^{7x + 4} = 3^{-3(x-3)}[/tex]
[tex]3^{7x + 4} = 3^{-3x + 9}[/tex]
Since both sides are now powers of 3, we can equal them:
[tex]7x + 4 = -3x + 9[/tex]
[tex]10x = 5[/tex]
[tex]x = \frac{5}{10}[/tex]
[tex]x = \frac{1}{2}[/tex]
The solution is [tex]x = \frac{1}{2}[/tex]
A helicopter is 2,500 feet above sea level. A pirate ship sunk with buried
treasure off the coast of Florida 125 years ago. It's depth is 3,000 feet
below the helicopter. How many feet below sea level is the pirate ship?
Answer:
500 feet below sea level
Step-by-step explanation:
You would take 2,500 and subtract 3,000 feet giving you an answer of -500 feet. Which means it is 500 feet below sea level
for triangle ABC with sides a,b and c the law of cosines states
c^2=
in which of the following cases must the law of cosines be used to solve a triangle?
ASA SSS SAS SSA
Option C is correct. The law of cosines must be used to solve a triangle in the case of SAS rule (Side Angle Side Rule)
For a triangle, ABC with sides a, b, and c respectively, the law of cosines is used on such a triangle if there is a presence of an angle between any two sides.
For example, if angle C is between the sides a and b, the equivalent cosine rule will be expressed as:[tex]c^2 = a^2 + b^2 + 2ab cos C[/tex]
Hence the law of cosines must be used to solve a triangle in the case of SAS rule (Side Angle Side Rule)
Learn more here: https://brainly.com/question/20880990
The base area of a rectangular prism is 56 square feet. If the height of the prism is 3 feet, what is the total volume of the prism (in cubic feet)?
NEED ANSWER ASAP WILL GIVE BRAINLIEST FOR CORRECT ANSWER
Answer:
y = 470 - 50x
Step-by-step explanation:
Total distance minus the distance covered in n number of hours if the speed is 50 mph.
what is the answer to this?
Answer:
i can only say that you should use this forumla, the sins law
sin(a)/A = sin(b)/B = sin(c)/C
Step-by-step explanation:
Consider the following data representing the price of laptop computers (in dollars). 1465, 1151, 1344, 1200, 1468, 1310, 1177, 1220, 1148, 1347, 1404, 1405, 1313, 1289, 1431, 1136, 1335, 1160, 1387, 1219, 1329 Price of Laptop Computers (in Dollars) Class Frequency Class Boundaries Midpoint Relative Frequency Cumulative Frequency 1132–1191 1192–1251 1252–1311 1312–1371 1372–1431 1432–1491 Step 3 of 7 : Determine the lower class boundary for the sixth class.
Solution :
Class Frequency Class boundaries Mid Relative Cumulative
point frequency frequency
1132-1191 5 1131.5-1191.5 1161.5 0.2381 5
1192-1251 3 1191.5-1251.5 1221.5 0.1428 8
1252-1311 2 1251.5-1311.5 1281.5 0.0952 10
1312-1371 5 1311.5-1371.5 1341.5 0.2381 15
1371-1431 4 1371.5-1431.5 1401.5 0.1905 19
1432-1491 2 1431.5-1491.5 1416.5 0.0952 21
Total 21
Therefore, the lower class boundary for the sixth class is 1431.5
Answer:
21
Step-by-step explanation:
1132-1191 5 1131.5-1191.5 1161.5 0.2381 5
1192-1251 3 1191.5-1251.5 1221.5 0.1428 8
1252-1311 2 1251.5-1311.5 1281.5 0.0952 10
1312-1371 5 1311.5-1371.5 1341.5 0.2381 15
1371-1431 4 1371.5-1431.5 1401.5 0.1905 19
1432-1491 2 1431.5-1491.5 1416.5 0.0952 21
please say i'm right
if the square is directly proportional to w and z =4 when w =8
Answer:
when you calculate the value of w is z= 5
Step-by-step explanation:
2. What type of sequence is this?
4,0-4,-8, -12,...
Arthimetic
Geometric
Neither
Answer:
Arithmetic
Step-by-step explanation:
Arithmetic is additive and geometric is multiplicative, and the numbers aren''t multiplying, they're adding.
In a fruit cocktail, for every 12ml of orange juice you need 8ml of apple juice and 50ml of coconut milk. What is the ratio of apple juice to coconut milk to orange juice expressed in its simplest form
Answer:
4:25:6 would be the simplest form
What is the mean absolute deviation of the following set of data?
4,6,12,8,10,10,7,8
A. Determine if the given figure is a polygon or not. Write P if it is a polygon
and NP if it is not.
Polygon: "a plane figure with at least three straight sides and angles, and typically five or more."
1. P
2. NP
3. P
4. NP
5. P
"A planar polygon is convex if it contains all the line segments connecting any pair of its points."
1. C
2. NC
3. NC
4. C
5. NC
Can someone please help me with this question
Answer:
volume= 186ft
Step-by-step explanation:
Questio
Matteo scored 85 on their first test, 89 on their second test, 85 on their third test, and
89 on their fourth test. Suppose Matteo has one more test in the semester and wants
to finish with a mean score of 88.
What score do they need on their last test to finish with a mean score of 88?
Answer:
He needs 92 on his last test.
Step-by-step explanation:
Mean score:
The mean is the sum of all scores divided by the number of tests.
In this question:
Scores of 85, 89, 85, 89 and x(the last one).
5 tests.
We want a mean of 88. So we find x for a mean of 88.
[tex]\frac{85 + 89 + 85 + 89 + x}{5} = 88[/tex]
[tex]348 + x = 440[/tex]
[tex]x = 440 - 348 = 92[/tex]
He needs 92 on his last test.
12 1/3 +6 2/5 reduce these into lowest terms
Answer:
18 11/15
Step-by-step explanation:
This is the answer because:
1) First, find the common denominator: 12 1/3 = 12 5/15 and 6 2/5 = 6 6/15
2) Then add the fractions: 12 5/15 + 6 6/15 = 18 11/15
3) 18 11/15 is reduced to the lowest terms because 11 is a prime number.
Therefore, 18 11/15 is the answer.
Hope this helps! :)
Answer:
52.7
Step-by-step explanation:
121/3= 40.33
62/5= 12.4
40.3+12.4=52.7
plz mark me as brainliest.
Child Health and Development Studies (CHDS) has been collecting data about expectant mothers in Oakland, CA since 1959. One of the measurements taken by CHDS is the weight increase (in pounds) for expectant mothers in the second trimester. In a fictitious study, suppose that CHDS finds the average weight increase in the second trimester is 14 pounds. Suppose also that, in 2015, a random sample of 45 expectant mothers have mean weight increase of 16.3 pounds in the second trimester, with a standard deviation of 5.9 pounds. A hypothesis test is done to see if there is evidence that weight increase in the second trimester is greater than 14 pounds. Find the p -value for the hypothesis test. The p -value should be rounded to 4 decimal places.
Answer:
0.9955
Step-by-step explanation:
Given :
Mean weight increase , μ = 14
Sample mean weight increase , xbar = 16.3
Standard deviation, s = 5.9
Sample size, n = 45
Hypothesis :
H0 : μ = 14
H1 : μ > 14
The test statistic : (xbar - μ) ÷ (s/sqrt(n))
Test statistic = (16.3 - 14) ÷ (5.9/sqrt(45))
Test statistic = 2.3 / 0.8795200
Test statistic = 2.615
The Pvalue :
P(Z < 2.615) = 0.99554
Hence, pvalue = 0.9955 (4 decimal places).