Solve normal distribution problem #11 9. The probability that a birth results in twins is estimated to be 0.016. Find the probability thatexactly 5 births out of 100 results in twins.9. The acceptance rate at a school is 34%. If 10 students apply, what is the probability that atmost 2 of them will be accepted? Assume independence between the students.Samples to use for Question 1010. Suppose a box contains 10 marbles: 4 blue and 6 red. You randomly draw two marbles withoutreplacement: if you draw two blue marbles, you win $10; if you draw two red marbles, you win$5. Otherwise, you win nothing. Let X denote your winnings. Find the distribution and theexpected value of X.10. A game of dice works as follows. You roll two dice. If the sum of the dice is 9, you win $9. Ifthe sum is at most 3, you win $12. Otherwise, you win nothing. Let X denote your winnings.Find the distribution and expected value of X.10. Suppose a box contains 8 marbles. 2 blue and 6 green. We draw two marbles without replace-ment. Let X denote the number of blue marbles drawn. Find the distribution and expectedvalue of X.Samples to use for Question 1111. Assume the finishing times for 5K male races are normally distributed with = 28 minutes andstandard deviation = 1.27 minutes.(a) Find the probability that a runner takes more than 30 minutes to finish a 5K race.(b) Suppose 10% of the runners took longer than William. How long did William take to finishthe race?MacBook Air

(a) The probability that a runner takes more than 30 minutes to finish 5K race is obtained below as…

Answered: 11. Assume the finishing times for 5K…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Solve normal distribution problem #11

9. The probability that a birth results in twins is estimated to be 0.016. Find the probability that
exactly 5 births out of 100 results in twins.
9. The acceptance rate at a school is 34%. If 10 students apply, what is the probability that at
most 2 of them will be accepted? Assume independence between the students.
Samples to use for Question 10
10. Suppose a box contains 10 marbles: 4 blue and 6 red. You randomly draw two marbles without
replacement: if you draw two blue marbles, you win $10; if you draw two red marbles, you win
$5. Otherwise, you win nothing. Let X denote your winnings. Find the distribution and the
expected value of X.
10. A game of dice works as follows. You roll two dice. If the sum of the dice is 9, you win $9. If
the sum is at most 3, you win $12. Otherwise, you win nothing. Let X denote your winnings.
Find the distribution and expected value of X.
10. Suppose a box contains 8 marbles. 2 blue and 6 green. We draw two marbles without replace-
ment. Let X denote the number of blue marbles drawn. Find the distribution and expected
value of X.
Samples to use for Question 11
11. Assume the finishing times for 5K male races are normally distributed with = 28 minutes and
standard deviation = 1.27 minutes.
(a) Find the probability that a runner takes more than 30 minutes to finish a 5K race.
(b) Suppose 10% of the runners took longer than William. How long did William take to finish
the race?
MacBook Air

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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