# Probability Distribution

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702)

On any given day the number of leasable square feet of office space available in a small city is a normally distributed random variable witha mean of 850,000 square feet and a standard deviation of 25,000 square feet.

The number of leasable square feet available in another city is normally distributed with a mean of

900,000 square feet and standard deviation of 25,000 square feet.

a. Sketch the distribution of leasable office space for both cities on the same graph.

b. What is the probability that the number of leasable square feet in the first city is less than 95,000 square feet?

c. What is the probability that the amount available in the second city is less than 925,000?

703)

The amount of money per month earned by an auditor with 10 years experience is a normally distributed random variable with mean $3500 and standard deviation $240.

a. What percentage of auditors with 10 years experience earn more than $4,000 a month?

b. What percentage of auditors with 10 years experience earn less than $3,200?

c. What is the probability that a randomly selected auditor earns between $3250 and $3800 per month?

d. What monthly income defines the top 10% of all auditors with 10 years experience?

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##### Solution Summary

The solution addresses on any given day the number of leasable square feet of office space available in a small city is a normally distributed random variable with a mean of 850,000 square feet and a standard deviation of 25,000 square feet.

The number of leasable square feet available in another city is normally distributed with a mean of

900,000 square feet and standard deviation of 25,000 square feet.

a. Sketch the distribution of leasable office space for both cities on the same graph.

b. What is the probability that the number of leasable square feet in the first city is less than 95,000 square feet?

c. What is the probability that the amount available in the second city is less than 925,000?

703)

The amount of money per month earned by an auditor with 10 years experience is a normally distributed random variable with mean $3500 and standard deviation $240.

a. What percentage of auditors with 10 years experience earn more than $4,000 a month?

b. What percentage of auditors with 10 years experience earn less than $3,200?

c. What is the probability that a randomly selected auditor earns between $3250 and $3800 per month?

d. What monthly income defines the top 10% of all auditors with 10 years experience?

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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