Question

1. The weight of people in a small town in Missouri is known to be normally distributed with a mean of 194 pounds and a standard deviation of 30 pounds. On a raft that takes people across the river, a sign states, “Maximum capacity 3,528 pounds or 18 persons.” What is the probability that a random sample of 18 persons will exceed the weight limit of 3,528 pounds? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

Probability =

2. A random sample is drawn from a normally distributed population with mean μ = 26 and standard deviation σ = 2.0.

a. Are the sampling distributions of the sample mean with n = 34 and n = 68 normally distributed?

• Yes, both the sample means will have a normal distribution.

• No, both the sample means will not have a normal distribution.

• No, only the sample mean with n = 34 will have a normal distribution.

• No, only the sample mean with n = 68 will have a normal distribution.

b. Calculate the probabilities that the sample mean is less than 26.6 for both sample sizes. (Round answers to 4 decimal places.)

	n Probability 34 68

3. At a new exhibit in the Museum of Science, people are asked to choose between 75 or 166 random draws from a machine. The machine is known to have 88 green balls and 82 red balls. After each draw, the color of the ball is noted and the ball is put back for the next draw. You win a prize if more than 60% of the draws result in a green ball.

a. Calculate the probability of getting more than 60% green balls. (Round your intermediate proportion values and “z” value to 2 decimal places, and final answer to 4 decimal places.)

75 Draws=

166 Draws=

Answer 1