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The amount of time that customers wait in line during peak hours at one bank is normally distributed with a mean of 13 minutes and a standard deviation of 3 minutes. The percentage of time that the waiting time lies between 11 and 13 minutes is equal to the area under the standard normal curve between ___ and ___.

Respuesta :

Answer:

It is between -067 and 0.

Step-by-step explanation:

In order to do the calculation, we employ the formula z score because random variables are standardized into z scores. Another name for the z score is standard score and its formula is as given below:

P(L ≤ x ≤ H) = P{[(L - H) ÷ SD] ≤ z ≤ [(H - H) ÷ SD]} ............ (1)

P = probability notation

L = Lower number = 11

H = Higher number = 13

SD = Standard deviation = 3

Substituting the above values into equation (1), we will obtain:

P(11 ≤ x ≤ 13) = P{[(11 - 13) ÷ 3] ≤ z ≤ [(13 - 13) ÷ 3]}

                    = P{[(-2) ÷ 3] ≤ z ≤ [0 ÷ 3]}

                    = P{-0.67 ≤ z ≤ 0}

Therefore, the percentage of time that the waiting time lies between 11 and 13 minutes is between -067 and 0 under the standard normal curve area.

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