Question

The sales data from the past two months of a frozen yogurt shop are approximately normal. The mean daily sales for the first month was $200 with a standard deviation of $30. On the 15th of the first month, the shop sold $245 of yogurt. The mean daily sales for the second month was $220 with a standard deviation of $50. On the 15th of the second month, the shop sold $270 of yogurt. Which month had a higher z-score for sales on the 15th, and what is the value of that z-score? a.) The second month, with a z-score of 1. b.) The second month, with a score of 1.67. c.) The first month, with a score of 0.9. d.) The first month, with a z-score of 1.5.

Answer 1

Answer: 1.5

Explanation:

Recall that .For the first month, .For the second month, .We can see the first month had the higher z-score of 1.5.

Answer 2

The correct option is D

Explanation:

From the question we are told that

The mean for the first month is
`\mu _ 1 = \$ 200`

The standard deviation for first month is
`\sigma_1 = \$ 30`

The sale on 15th of first month is
`x_1 = \$245`

The mean for the second month is
`\mu _ 2 = \$220`

The standard deviation for second month is
`\sigma_2 = \$ 50`

The sale on 15th of second month is
`x_2 = \$ 270`

Generally the z-score is mathematically represented as

`z = (x - \mu )/( \sigma)`

For the first month

`z_1 = (x_1 - \mu_1 )/( \sigma_1 )`

`z_1 = ( 245 - 200 )/( 30 )`

`z_1 = 1.5`

For the second month

`z_1 = (x_2 - \mu_2 )/( \sigma_2 )`

`z_1 = ( 270 - 220 )/( 50 )`

`z_1 = 1`