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:

The  correct option is D

Step-by-step 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

         $z = \frac{x - \mu }{ \sigma}$

For the  first month  

         $z_1 = \frac{x_1 - \mu_1 }{ \sigma_1 }$

         $z_1 = \frac{ 245 - 200 }{ 30 }$

         $z_1 = 1.5$

For the second  month

         $z_1 = \frac{x_2 - \mu_2 }{ \sigma_2 }$

         $z_1 = \frac{ 270 - 220 }{ 50 }$

         $z_1 = 1$