Question

A) A local bakery has determined a probability distribution for the number of cheesecakes that they sell in a given day. Let xx equal the number of cheesecakes sold on a randomly selected day.

xx
	0	5	10	15	20
P(x)P(x)	0.12	0.29	0.35	?	0.1

What is the probability of selling 15 cheesecakes in a given day?

P(x=15)=P(x=15)=

What is the probability of selling at least 10 cheesecakes?

P(x≥10)=P(x≥10)=

What is the probability of selling 5 or 15 cheesecakes?

P(x=5P(x=5 or x=15)=x=15)=

What is the probability of selling 25 cheesecakes?

P(x=25)=P(x=25)=

What is the probability of selling at most 10 cheesecakes?

P(x≤10)=P(x≤10)=

Give the expected number of cheesecakes sold on any given day using the discrete probability distribution?

μ=μ=

B)

Consider the discrete random variable XX given in the table below. Calculate the mean, variance, and standard deviation of XX. Also, calculate the expected value of XX. Round solution to three decimal places, if necessary.

xx	6	7	9	20
P(x)P(x)	0.09	0.7	0.14	0.07

μμ =


σ2σ2 =


σσ =


What is the expected value of XX?

E(X)=E(X)=

C)

The probability distribution for the number of students in statistics classes at IRSC is given, but one value is missing. Fill in the missing value, then answer the questions that follow. Round solutions to three decimal places, if necessary.

xx	P(x)P(x)
26	0.1
27	0.14
28	0.17
29
30	0.12

Find the mean number of students in a Statistics class at IRSC:
μ=μ=  

Find the standard deviation of the number of students in a Statistics class at IRSC:
σ=σ=  

D)

The following table gives the probability distribution of a discrete random variable XX. Use the table to find the following probabilities. Round solutions to three decimal places, if necessary.

xx	P(x)P(x)
0	0.286
1	0.271
2	0.157
3	0.129
4	0.086
5	0.071

P(x=2)=P(x=2)=

P(x≤4)=P(x≤4)=

P(x≥1)=P(x≥1)=

P(1≤x≤3)=P(1≤x≤3)=

The shape of the probability distribution is Select an answer uniform skewed left symmetric skewed right  .

E)

The following table gives the frequencies of the nest size (number of eggs) of 199 Great Blue Heron nests recorded on a recent survey in Indian River County. Use the data to construct a discrete probability distribution.

xx	0	1	2	3	4	5
ff	7	45	50	34	20	43

Construct the probability distribution of xx, where xx is the number of eggs in a randomly selected Great Blue Heron nest in Indian River County. Round solutions to three decimal places, if necessary.

xx	0	1	2	3	4	5
P(x)P(x)

F)

A large fast-food restaurant is having a promotional game where game pieces can be found on various products. Customers can win food or cash prizes. According to the company, the probability of winning a prize (large or small) with any eligible purchase is 0.116.

Consider your next 33 purchases that produce a game piece. Calculate the following:

This is a binomial distribution. Round your answers to 4 decimal places.

a) What is the probability that you win 4 prizes?

b) What is the probability that you win more than 5 prizes?

c) What is the probability that you win between 3 and 5 (inclusive) prizes?

d) What is the probability that you win 3 prizes or fewer?

Answer 1