Question

# 1.The capacity of an elevator will be exceeded if 10 people have mean weights greater...

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.
1. 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.

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

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