Question

Do you want to own your own candy store? Wow! With some interest in running your own business and a decent credit rating, you can probably get a bank loan on startup costs for franchises such as Candy Express, The Fudge Company, Karmel Corn, and Rocky Mountain Chocolate Factory. Startup costs (in thousands of dollars) for a random sample of candy stores are given below. Assume that the population of x values has an approximately normal distribution.

Answer 1

`\bar x = 107.11`

`\sigma_x = 31.07`

Explanation:

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Given

`x: 97\ 178\ 129\ 90\ 75\ 94\ 116\ 100\ 85`

Solving (a): The sample mean

This is calculated using:

`\bar x = (\sum x)/(n)`

So, we have:

`\bar x = (97+ 178+ 129+ 90+ 75+ 94+ 116+ 100+ 85)/(9)`

`\bar x = (964)/(9)`

`\bar x = 107.11`

Solving (b): The sample standard deviation

This is calculated as:

`\sigma_x = \sqrt{(\sum(x - \bar x)^2)/(n-1)}`

So, we have:

`\sigma_x = \sqrt{((97 - 107.11)^2 +.............+ (85- 107.11)^2 )/(9-1)}`

`\sigma_x = \sqrt{(7720.8889)/(8)}`

`\sigma_x = √(965.1111125)`

`\sigma_x = 31.07`