Question

A large call center outside a city tracks the number of phone calls recieved each day. The daily number of phone calls recieved is normally distributed with μ = 152 μ = 152 and σ = 6.2 σ = 6.2 .

Find the probability that on a randomly selected day the number of phone calls received is between 152 and 154.

P(152 < X < 154) =

Find the probability that a random sample of n = 25 n = 25 days has a mean number of phone calls recieved between 152 and 154.

P(152 < M < 154) =

Enter your answers as numbers accurate to 3 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

Let X denote the number of phone calls received each day. Then,

a)

b)

Using Central Limit theorem, we know,