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.

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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...

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Suppose that the speed at which cars go on the freeway is normally distributed with mean 79 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( 79 5 or or b. If one car is randomly chosen, find the probability that it is traveling more than 78 mph. Round to 4 decumal places. c. If one of the cars is randomly chosen, find the probability that it is traveling between 81 and 86 mph. Round to 4 decimal places.
3. In a job fair, 3 000 applicants applied for a job. Their mean age was found to be 28 with a standard deviation of 4 years. a) Draw a normal curve distribution showing the z-scores and the raw scores. b) How many applicants are below 20 years old? c) How many applicants are above 32 years old? d) How many have ages between 24 and 32 years? ·e) Find the ages such that 75% is below it. 5. Five hundred children participated in a field demonstration. Their heights averaged 110 cm with standard deviation of 6 cm. a) What is the probability that a child, picked at a random, has a height greater than 116 cm? b) What is the probability that the height of a child picked at a random, is less than 104 cm. c) How many children belong to the upper 15% of the group?
5. The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of 10. Suppose that one individual is randomly chosen. Let X = percent of fat calories. Find the probability that the percent of fat calories a person consumes is more than 40. Sketch the associated graph/figure. Find the maximum number for the lower quarter of percent of fat calories. Sketch the graph, and write the probability statement (i.e. interpret calculated value).
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
The following table shows the number of people that are either 18, 19, 20 or 21 years old, from a sample of 258 people. a) Complete the table. Age Number of people 18 54 19 69 20 70 21 (b Find the mean for this sample. Give your answer to at least 2 decimal places. (c Find the standard deviation for this sample. Give your answer to at least 2 decimal places.
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)
he mean height of an adult giraffe is 18 feet. Suppose that the distribution is normally distributed with standard deviation 0.8 feet. Let X be the height of a randomly selected adult giraffe. Round all answers to 4 decimal places where possible.b. What is the median giraffe height? ft.c. What is the Z-score for a giraffe that is 19 foot tall? d. What is the probability that a randomly selected giraffe will be shorter than 17.1 feet tall? e. What is the probability that a randomly selected giraffe will be between 17.3 and 17.9 feet tall? f. The 90th percentile for the height of giraffes is ft.
A normal distribution of scores has a standard deviation of 10 and a mean of 0. Find the z-scores corresponding to each of the following values: a) A score that is 20 points above the mean. b) A score that is 10 points below the mean. c) A score that is 15 points above the mean d) A score that is 30 points below the mean. IQ scores have a mean of 100 and a standard deviation of 16. Albert Einstein reportedly had an IQ of 160. a. Convert Einstein’s IQ score to a z score.
III. SAMPLING AND SAMPLING DISTRIBUTIONS Assume that the systolic blood pressure of 30-year-old males is normally distributed, with an average of 122 mmHg and a standard deviation of 10 mmHg. а. b. Calculate the probability that the blood pressure of an individual male from this population will be between 118 and 124 mmHg.

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