Answer:
0.68269
Step-by-step explanation:
When we are to find the z score for population where a random sample is picked, the z.score formula we use is
z = (x-μ)/Standard error, where
x is the raw score,
μ is the population mean
Standard error = σ/√n
σ is the population standard deviation
n = random number of samples
For : x = 38 minutes, μ = 40, σ = 10, n = 5
z = 38 - 40/10 /√25
= -2/10/5
= -2/2
= -1
Determining the probability value using z table
P(x = 38) = P(z = -1)
= 0.15866
For : x = 42 minutes, μ = 40, σ = 10, n = 25
z = 42 - 40/10 /√25
= 2/10/5
= 2/2
= 1
Determining the probability value using z table
P(x = 42) = P(z = 1)
= 0.84134
The probability that their average waiting time will be between 38 and 42 minutes is calculated as
P(-Z<x<Z)
= P(-1 < x < 1)
= P(z = 1) - P(z = -1)
= 0.84134 - 0.15866
= 0.68269
Therefore, the probability that their average waiting time will be between 38 and 42 minutes is 0.68269
