The overhead reach distances of adult females are normally distributed with a mean of

202.5 cm202.5 cm

and a standard deviation of

8 cm8 cm.

a. Find the probability that an individual distance is greater than

215.00215.00

cm.b. Find the probability that the mean for

2020

randomly selected distances is greater than 201.00 cm.201.00 cm.

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

a. The probability is

nothing.

​(Round to four decimal places as​ needed.)

b. The probability is

nothing.

​(Round to four decimal places as​ needed.)

c. Choose the correct answer below.

A.

The normal distribution can be used because the finite population correction factor is small.

B.

The normal distribution can be used because the mean is large.

C.

The normal distribution can be used because the original population has a normal distribution.

D.

The normal distribution can be used because the probability is less than 0.5

Click to select your answer(s).

32. Every day, Jorge buys a lottery ticket. Each ticket has a probability of 0.3 of winning a prize. After seven days, what is the probability that Jorge has won at least one prize? Round your answer to four decimal places.

26. Charles has seven songs on a playlist. Each song is by a different artist. The artists are Shania Twain, Nick Carter, Aaron Carter, Joey McIntyre, Phil Collins, Shakira, and Michael Jackson. He programs his player to play the songs in a random order, without repetition. What is the probability that the first song is by Nick Carter and the second song is by Joey McIntyre? Write your answer as a fraction or a decimal, rounded to four decimal places.

25. An unfair coin has probability 0.3 of landing heads. The coin is tossed seven times. What is the probability that it lands heads at least once? Round the answer to four decimal places.

21. Let A and B be events with =PA0.7 and =PB0.5. Assume that A and B are independent. Find PA and B.

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 171 lb. The new population of pilots has normally distributed weights with a mean of 138 lb and a standard deviation of 31.6 lb.

a. If a pilot is randomly​ selected, find the probability that his weight is between 130 lb and 171 lb.

The probability is approximately ?

​(Round to four decimal places as​ needed.)

b. If 37 different pilots are randomly​ selected, find the probability that their mean weight is between 130 lb and 171 lb.

The probability is approximately = ?

​(Round to four decimal places as​ needed.)

c. When redesigning the ejection​ seat, which probability is more​ relevant?

A.

Part​ (b) because the seat performance for a sample of pilots is more important.

B.

Part​ (b) because the seat performance for a single pilot is more important.

C.

Part​ (a) because the seat performance for a sample of pilots is more important.

D.

Part​ (a) because the seat performance for a single pilot is more important.

Assume a normal distribution and find the following probabilities.

(Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)

(a) P(x < 25 | μ = 27 and σ = 3)
enter the probability of fewer than 25 outcomes if the mean is 27and the standard deviation is 3

(b) P(x ≥ 75 | μ = 60 and σ = 8)
enter the probability of 75or more outcomes if the mean is 60and the standard deviation is 8

(c) P(x > 57 | μ = 60 and σ = 5)
enter the probability of more than 57outcomes if the mean is 60and the standard deviation is 5

(d) P(19 < x < 27 | μ = 25 and σ = 3)
enter the probability of more than 19and fewer than 27outcomes if the mean is 25and the standard deviation is 3

(e) P(x ≥ 85 | μ = 70 and σ = 1.86)
enter the probability of 85or more outcomes if the mean is 70and the standard deviation is 1.86

Capital injection as a screening device. Suppose we have a firm that needs $200 to invest in a project that will yield a random payoff one period hence and that the lender will require 10% loan rate. The firm knows the probability distribution of the project’s cash flow, but no one else does. All that others know is that the project can be type C or type D. If it is type C, then it will yield a cash flow of $300 with probability 0.9 and zero with probability of 0.1. If it is type D, the project will yield a cash flow of $600 with probability 0.5 and zero with probability 0.5.

The corporate tax rate is now 20%. Now though bank cannot tell whether the borrower has a type C or a type D project, the bank wish to separate out each type of borrower correctly. The key to resolving this informational asymmetry is to use capital from the borrower as a signal. As a banker, how would you deal with those borrowers, assuming that the borrower type is either project C or project D?

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 171 lb. The new population of pilots has normally distributed weights with a mean of 138 lb and a standard deviation of 34.8 lb.

a. If a pilot is randomly​ selected, find the probability that his weight is between 130 lb and 171 lb.

The probability is approximately________. ​

(Round to four decimal places as​ needed.)

b. If 37 different pilots are randomly​ selected, find the probability that their mean weight is between 130 lb and 171 lb.

The probability is approximately________.

​(Round to four decimal places as​ needed.)

c. When redesigning the ejection​ seat, which probability is more​ relevant?

A. Part​ (b) because the seat performance for a sample of pilots is more important.

B. Part​ (b) because the seat performance for a single pilot is more important.

C. Part​ (a) because the seat performance for a single pilot is more important.

D. Part​ (a) because the seat performance for a sample of pilots is more important.

A survery of New York Dentists shows the cost of a certain dental procedure is normally distributed with a mean cost of $350 and a standard deviation of $40. Be sure convert your analysis from dollars to z-scores. ( Answer the following probability quesitons using Excel and show your work.

A, Draw a Picture( by hand) of the probability density function and mark the x axis in dollars with values from 1,2, and 3 standard deviations above and below the mean.

b. If you pick a dentist at random, What is the probability this procedure will cost less than $300?

C. What is the probability the cost will be greater than $400? ( Are you surprised between your answers to b and C?

D. What is the Probability the cost will be between $310 and $410?

E. One Dentist claims he is cheaper than 95% of all dentist in New York. What would he charge for this procedure if he is telling the truth?

F. what range of cost would be considered outliers?

The weights of a certain brand of candies are normally distributed with a mean weight of 0.8541 g and a standard deviation of

0.0516 g. A sample of these candies came from a package containing 440 ​candies, and the package label stated that the net weight is 375.5 g.​ (If every package has 440 ​candies, the mean weight of the candies must exceed 375.5/440 =0.8534 g for the net contents to weigh at least 375.5 g.)

a. If 1 candy is randomly​ selected, find the probability that it weighs more than 0.8541 g.

The probability is _______.

​(Round to four decimal places as​ needed.)

b. If 440 candies are randomly​ selected, find the probability that their mean weight is at least 0.8541 g.

The probability that a sample of 440 candies will have a mean of 0.8541g or greater is

______________.

​(Round to four decimal places as​ needed.)

c. Given these​ results, does it seem that the candy company is providing consumers with the amount claimed on the​ label?

Yes, because the probability of getting a sample mean of 0.8541g or greater when 440 candies are selected is not exceptionally small.

Assume a normal distribution and find the following probabilities.

(Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)

(a) P(x < 17 | μ = 20 and σ = 3)
enter the probability of fewer than 17 outcomes if the mean is 20 and the standard deviation is 3

(b) P(x ≥ 61 | μ = 50 and σ = 8)
enter the probability of 61 or more outcomes if the mean is 50 and the standard deviation is 8

(c) P(x > 45 | μ = 50 and σ = 5)
enter the probability of more than 45 outcomes if the mean is 50 and the standard deviation is 5

(d) P(16 < x < 19 | μ = 18 and σ = 3)
enter the probability of more than 16 and fewer than 19 outcomes if the mean is 18 and the standard deviation is 3

(e) P(x ≥ 75 | μ = 60 and σ = 2.79)
enter the probability of 75 or more outcomes if the mean is 60 and the standard deviation is 2.79

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150 lb and 191 lb. The new population of pilots has normally distributed weights with a mean of 156 lb and a standard deviation of 34.9 lb

a. If a pilot is randomly​ selected, find the probability that his weight is between 150 lb and 191 lb.The probability is approximately_____.

​(Round to four decimal places as​ needed.)

b. If 39 different pilots are randomly​ selected, find the probability that their mean weight is between 150 lb and 191 lb.The probability is approximately_____.

​(Round to four decimal places as​ needed.)

c. When redesigning the ejection​ seat, which probability is more​ relevant?

A. Part​ (b) because the seat performance for a single pilot is more important.

B. Part​ (a) because the seat performance for a sample of pilots is more important.

C. Part​ (b) because the seat performance for a sample of pilots is more important.

D. Part​ (a) because the seat performance for a single pilot is more important.