A population of 29 yearold males has a mean salary of 29321

A population of 29 year-old males has a mean salary of $29,321 with a standard deviation of S2,120. If a sample of 100 men is taken, what is the probability their mean salaries will be less than S29.000? You are going to flip 5 \'fair\' coins. You are interested in the number of \'heads\' you sec when you flip the 5 coins, let X represent the number of heads you observe in the flip of 5 coins. List the sample space. Give the probability distribution of X. What is the probability you observe at most 1 head? What is P (X > 4)? What is the average number of heads you would expect to see? What is the standard deviation? In a certain game of chance, your chances of losing are 0.4. Assume outcomes are independent and that you will play the game seven times. What is the probability that you win at most once? What is the probability that you win all seven times? For example, say that a statistical study claims that 0.38 or 38% of all the students taking the ACT text would like math help. Suppose you take a random sample of 100 students. What is the probability that more than 45% of them say they need math help? Sixteen adult males approach an elevator on the 100th floor of Everett Tower. The elevator has the sign: They enter the elevator. Find the probability that the cable snaps and they plunge to their death- i.e.. their combined weight exceed 2900 pound. Use the fact that the mean weight of an adult male is 170 pounds and the standard deviation is 15 pounds.

Solution

a) X is the no of heads we get in tossing 5 coins

Sample spae will have 2^5 = 32 outcomes

b) Pdf of x is binomial (5, 0.5)

c) P(X<=1) = 0.1875

d) P(X>=4) =0.1875

e) Average =np = 2.5

Variance = npq =1.25

std dev =1.118

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3) X no of wins is binomial with (7,0.6)

a) P(x<=1) =0.0188

b) P(x=7) = 0.02799