Answer:
Step-by-step explanation:
Let x represent the amount of time to prepare and deliver a pizza from Pepe's pizza. Since it is normally distributed and the population standard deviation is known, we would calculate the z score by applying the formula,
z = (x - μ)/σ
where
σ is the population standard deviation
μ is the population mean
x is the sample mean
From the information given,
μ = 20
σ = 5
a) We want to find P(20 < x < 35)
For x = 20.
z = (20 - 20)/5 = 0
From the normal distribution table, the area t the left of z = 0 is 0.5
For x = 20.
z = (20 - 20)/5 = 0
From the normal distribution table, the area to the left of z = 0 is 0.5
For x = 35.
z = (35 - 20)/5 = 3
From the normal distribution table, the area to the left of z = 3 is 0.9987
P(20 < x < 35) = 0.9987 - 0.5 = 0.4987
between 20 and 35 minutes = 0.4987
b)We want to find P(x < 18)
For x = 18,
z = (18 - 20)/5 = - 0.4
From the normal distribution table, the area to the left of z = - 0.4 is 0.3446
in less than 18 minutes = 0.3446
c) We want to find P(x > 24)
P(x > 24) = 1 - P(x ≤ 24)
For x = 24,
z = (24 - 20)/5 = 0.8
From the normal distribution table, the area to the left of z = 0.8 is 0.7881
P(x > 24) = 1 - 0.7881
P(x > 24) = 0.2119
in more than 24 minutes = 0.2119