# Statistics - Probability

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1) A record store owner wants to determine consumer tastes. She decides to observe customers in her store on a particular day and record the number of minutes the each spends in the Alternative Music and Rap sections of the store. She came up with the following data:

Alternative Music Rap

Mean = x = 25 Mean = 20

Standard Dev = 3 Standard Dev = 2

a) What is the probability that a customer spends between 25 and 35 minutes in the Alternative Music section?

b) What is the probability that a customer spends between 20 and 25 minutes in the Rap section?

2) The same store owner above wanted to better understand her profits. She observed that her profits over the last few years are normally distributed with a mean of $100,000 and a standard deviation of $10,000.

(a) What is the probability that her store will make more than $125,000 this year?

(b) What is the probability that she makes more than $95,000 this year?

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The probability consumer tastes are examined in statistics. The solution answers the question(s) below.

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1) A record store owner wants to determine consumer tastes. She decides to observe customers in her store on a particular day and record the number of minutes the each spends in the Alternative Music and Rap sections of the store. She came up with the following data:

Alternative Music Rap

Mean = x = 25 Mean = 20

Standard Dev = 3 Standard Dev = 2

a) What is the probability that a customer spends between 25 and 35 minutes in the Alternative Music section?

Solution. Assume that it follows the normal distribution. Let TM be the time a customer spends in the Alternative Music ...

###### 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!"
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- "Thank you very much for your valuable time and assistance!"

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