the indicated probabilities using the geometric​ distribution, the Poisson​ distribution, or the binomial distribution. Then determine if the events are unusual. If​ convenient, use the appropriate probability table or technology to find the probabilities. The mean number of births per minute in a country in a recent year was about seven. Find the probability that the number of births in any given minute is​ (a) exactly six​, ​(b) at least six​, and​ (c) more than six. ​(a) P(exactly six​)= enter your response here ​(Round to four decimal places as​ needed.)

Using the Poisson distribution, it is found that the probabilities are:

a) 0.149

b) 0.6993

c) 0.5503

We are given only the mean, hence, the Poisson distribution is used.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

The mean is of 7 births per minute, hence [tex]\mu = 7[/tex].

Item a:

The probability is P(X = 6), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 6) = \frac{e^{-7}(7)^{6}}{(6)!} = 0.149[/tex]

Item b:

This probability is:

[tex]P(X \geq 6) = 1 - P(X < 6)[/tex]

In which:

[tex]P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]

Following the logic used in item a to find each probability, we have that [tex]P(X < 6) = 0.3007[/tex], hence:

[tex]P(X \geq 6) = 1 - P(X < 6) = 1 - 0.3007 = 0.6993[/tex]

Item c:

This probability is:

[tex]P(X > 6) = 1 - P(X \leq 6)[/tex]

[tex]P(X \leq 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)[/tex]

We have that [tex]P(X \leq 6) = 0.4497[/tex], hence:

[tex]P(X > 6) = 1 - P(X \leq 6) = 1 - 0.4497 = 0.5503[/tex]

A similar problem is given at https://brainly.com/question/16912674

Heights of women have a bell-shaped distribution with a mean of 161 cm and a standard deviation of 7 cm. What percent of women fall between 154 cm and 182 cm

If the silver accounts for 84% of the bar's weight, what is the weight of the silver?

Please answer!! Only if your answer is correct though.

Could I get help…………

What’s 100/100 in simplest form

In which of these situations would the answer to the
question be 0?
A) The low temperature one day was -10°F. The high
temperature that day was 10 F. What is the difference
between the low temperature and the high temperature
that day?
B) A trail to walk up a hill begins at an elevation -16 yards.
The trail ends at an elevation of 16 yards. By how many
yards does the elevation of the trail change from
beginning to end?
C) Justine left her grandmother's house and walked 3
blocks directly south. Then she walked 3 blocks directly
north. At this point, how many blocks was Justine from
her grandmother's house?
D) Theodore jumped into a pool from a diving board 10
feet above the water. He sank 10 feet and then swam
straight up to the surface of the water. How many feet
did Theodore swim?

What property is -5(-9x^2+8)+20=10x^2-15

-2 5/12 - (-10 8/9)

What is the equation of this line?

- C C) C.P = Rs 20, profit Rs 2, S
.P. -​

Given f(x) and g(x) are inverse functions. If f(-2)=1 then g(1)=-2

True

False

СЕ
What is the product of
(5m2) (2m -3)
7
7m6
10
10m6

Kiran wants to buy blueberries and raspberries to make a fruit tart. Blueberries cost $3.25 per pound and raspberries cost $2.50 per pound. How many pounds of fruit does he buy if he buys 2 pounds of blueberries and 1.5 pounds of raspberries? How many pounds of fruit does he buy if he buys x pounds of blueberries and y pounds of raspberries?

the value of x in the solution to the system x+y=10 and x-y=4

A shoe box in the shape of a rectangular prism has these dimensions 14in,8 1/2in,4 3/4inwhat is the volume

-6x - 3= 27
Help pless ​

The expression 63+81,
How can you can use the distributive property in the GCF to find a equivalent expression? Explain how can you check your answer

3/15 as an improper fraction

I will mark brainlist
Find the geometric mean between 18 and 7. Write your answer in radical form.



• 3 square root of 14


• 126



• 9 square root of 7



• 128

A​ 12-sided die is rolled. The set of equally likely outcomes is​ {1,2,3,4,5,6,7,8,9,10,11,12}. Find the probability of rolling a number greater than 7

Paul was thinking of a number. Paul adds 1.2 to the number the doubles the result to get an answer of 68.3. Form an equation with x from the information​

It takes 10 pounds of potatoes to make 15 pounds of mashed potatoes. At this rate, how many pounds of mashed potatoes can be made with 15 pounds of potatoes?

2
Technology required. A plane leaves the ground with an elevation angle of 6 degrees.
The plane travels 10 miles horizontally.
a. How high is the plane at the time?
b. What is the distance of the plane's path?
Round answers to the nearest tenths.
How high is the plane at this time?
miles
What is the distance of the plane's path?
miles

how to solve subtraction of percentage from whole numbers​

Without graphing, classify the system of equations as either consistent or inconsistent.
−7x+8y=9

21x/8−3y=−6

-8-8-6-2 4 12 22
What is the nth term rule of the quadratic sequence

Determine the period of the following graph.

help me due today it is math

help me plz!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

helpppppppppp WILLLL GIVE BRAINLISTTTTT