Mario's Pizza delivers pizzas within a 10-mile radius of the restaurant. Their delivery times are Normally distributed with a mean delivery time of 30 minutes and a standard deviation of 10 minutes. Find the probability that a randomly selected customer will have to wait a) less than 25 minutes b) more than 38 minutes c) between 26 and 32 minutes

a) 0.30854

b) 0.21186

c) 0.23468

Step-by-step explanation:

Mario's Pizza delivers pizzas within a 10-mile radius of the restaurant. Their delivery times are Normally distributed with a mean delivery time of 30 minutes and a standard deviation of 10 minutes.

We solve using z score formula.

z = (x-μ)/σ, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

Find the probability that a randomly selected customer will have to wait

a) less than 25 minutes

for x < 25 minutes

z = 25 - 30/10

z = -0.5

Probability value from Z-Table:

P(x<25) = 0.30854

b) more than 38 minutes

For x > 38 minutes

z = 38 - 30/10

z =0.8

Probability value from Z-Table:

P(x<38) = 0.78814

P(x>38) = 1 - P(x<38) = 0.21186

c) between 26 and 32 minutes

For x = 26 minutes

z = 26 - 30/10

z = -0.4

Probability value from Z-Table:

P(x = 26) = 0.34458

For x = 32 minutes

z = 32 - 30/10

z = 0.2

Probability value from Z-Table:

P(x = 32) = 0.57926

The probability that a randomly selected customer will have to wait between 26 and 32 minutes is calculated as:

P(x = 32) - P(x = 26)

= 0.57926 - 0.34458

= 0.23468