15. Heights of men in America have a normal distribution with a mean of 69.5 9 inches and astandard deviation of 3 inches. Perform the following calculations.a) In a random sample of 20 adult men in the US, find P(68 < X < 70).b) If 100 American men are chosen at random, find the probability that at least 25 of them areshorter than 68 inches. Hint, let Y be the number of Americans shorter than 68, then Y isbinomial. Find the probability using a normal approximation.16. Let X1, X100 be a random sample from a distribution with pdff(x)=(3x²2+x, 0≤x≤ 1otherwisea) Find the mean of Xb) Find the variance of Xc) Use the CLT to find the probability of P(0.7< X <0.75.

As per guidelines we will solve the first question only, please repost other questions for more…

Answered: 15. Heights of men in America have a…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

8) Scores on an exam have a normal distribution with a mean of 125 and a standard deviation of 19. Be sure to draw the normal distribution and shade the are being found. a) Find the probability that a person would score above 129 b) Find the probability that a person would score between 123 and 151. c) Find the probability that a group of 7 people would have a mean score above 130. d) Find the score needed to be in the top 10% of the class.
Suppose that the speed at which cars go on the freeway is normally distributed with mean 67 mph and standard deviation 9 miles per hour. Let X be the speed for a randomly selected car.a. What is the distribution of X? X ~ N( ? , ? )b. If one car is randomly chosen, find the probability that it is traveling more than 65 mph. Round to 4 decumal places. ?c. If one of the cars is randomly chosen, find the probability that it is traveling between 69 and 74 mph. Round to 4 decimal places. ?
An elevator has a placard stating that the maximum capacity is 4400 lb-29 passengers. So, 29 adult male passengers can have a mean weight of up to 4400/29 = 152 pounds. Assume that weights of males are normally distributed with a mean of 180 lb and a standard deviation of 29 lb. a. Find the probability that 1 randomly selected adult male has a weight greater than 152 lb. b. Find the probability that a sample of 29 randomly selected adult males has a mean weight greater than 152 lb. c. What do you conclude about the safety of this elevator? a. The probability that 1 randomly selected adult male has a weight greater than 152 lb is ☐ (Round to four decimal places as needed.)
The number of ants per acre in the forest is normally distributed with mean 42,000 and standard deviation 12,221. Let X = number of ants in a randomly selected acre of the forest. Round all answers to 4 decimal places where possible. b. Find the probability that a randomly selected acre in the forest has fewer than 32,793 ants. c. Find the probability that a randomly selected acre has between 46,676 and 51,692 ants. d. Find the first quartile. ? ants (round your answer to a whole number) PLEASE ANSWER THE 3 SUBS B, C AND D
3. Assume the heights of students at Champlain College are normally distributed with a mean of 64.0 inchesand a standard deviation of 1.2 inches. Which of the following values best approximates the probabilityof randomly selecting a Champlain College studenttallerthan 62.2 inches?A. 0.0668B. 0.0359C. 0.9332D. 0.9641E. 1.0155
With the diagram please
38)
Suppose that the speed at which cars go on the freeway is normally distributed with mean 80 mph and standard deviation 10 miles per hour. Let X be the speed for a randomly selected car. a. What is the distribution of X? X - N( b. If one car is randomly chosen, find the probability that it is traveling more than 79 mph. Round to 4 decumal places. c. If one of the cars is randomly chosen, find the probability that it is traveling between 83 and 86 mph. Round to 4 decimal places.
An elevator has a placard stating that the maximum capacity is 4100 lb-27 passengers. So, 27 adult male passengers can have a mean weight of up to 4100/27= 152 pounds. Assume that weights of males are normally distributed with a mean of 185 lb and a standard deviation of 29 lb. a. Find the probability that 1 randomly selected adult male has a weight greater than 152 lb. b. Find the probability that a sample of 27 randomly selected adult males has a mean weight greater than 152 lb. c. What do you conclude about the safety of this elevator? Round to four decimal places as needed
5. The mean birth weight for babies born one month early is 2630 grams. Assume that the population has a standard deviation of 220 grams. Sketch the distribution of birth weights (in grams) of children born one month early. Calculate probability of a child born one month early with a birth weight between 2100 grams and 2900 grams. Find the weight which corresponds to the top 25% of birth weights for babies born one month early.
A population has a normal distribution with a mean of 32.9 and a standard deviation of 35.2. Draw 4. a normal curve with labels, shading, and what you entered into the calculator for full credit. Round your answer to 4 decimal places. Find the probability that a randomly selected item is between 27.5 and 40.6 a) Find the probability that a sample size of 25 is randomly selected and is less than 28.2. b)
Suppose that the speed at which cars go on the freeway is normally distributed with mean 76 mph and standard deviation 5 miles per hour. Let X be the speed for a randomly selected car.a. What is the distribution of X? X ~ N( ? , ? )b. If one car is randomly chosen, find the probability that it is traveling more than 74 mph. Round to 4 decumal places. c. If one of the cars is randomly chosen, find the probability that it is traveling between 79 and 85 mph. Round to 4 decimal places.

SEE MORE QUESTIONS

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS