Question

   1.The capacity of an elevator will be exceeded if 10 people have mean weights greater than 167 pounds. Suppose the people have weights that are normally distributed with a mean of 165 pounds with a standard deviation of 21 pounds. Please write your answer in a complete sentence and draw a sketch. Use Table A-2.

1. Find the probability that if a person is randomly chosen his weight will be greater than 170 pounds.

2. Find the probability that 10 randomly selected people will have a sample mean weight that is greater than 180 pounds.

2a. If the mean salary is $60,000 and the standard deviation is $3,900, what is the salary range of the middle 64 % of the workforce if the salaries are normally distributed? Draw a sketch and write your answer in a complete sentence. Also please use Table A-2.

2b. Determine the salary that separates the bottom 3.75% and the salary that separates the top 3.75% of the workforce. Draw a sketch and write your answer in a complete sentence. Also please use Table A-2.

Answer 1

Solution:-

1)

Mean = 165, S.D = 21

a) The probability that if a person is randomly chosen his weight will be greater than 170 pounds is 0.4059.

x = 170

By applying normal distribution:-

z = 0.2381

P(z > 0.2381) = 0.4059

b) The probability that 10 randomly selected people will have a sample mean weight that is greater than 180 pounds is 0.2375.

x = 180

By applying normal distribution:-

z = 0.7143

P(z > 0.7143) = 0.2375