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.

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

- 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**

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