Answer: the probability that John’s drive to work will take between 36 and 40 minutes is 0.32
Step-by-step explanation:
Since the distribution of driving times is approximately normal, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = driving times.
µ = mean time
σ = standard deviation
From the information given,
µ = 38 minutes
σ = 5 minutes
The probability that John’s drive to work will take between 36 and 40 minutes is expressed as
P(36 ≤ x ≤ 40)
For x = 36,
z = (36 - 38)/5 = - 0.4
Looking at the normal distribution table, the probability corresponding to the z score is 0.34
For x = 40,
z = (40 - 38)/5 = 0.4
Looking at the normal distribution table, the probability corresponding to the z score is 0.66
Therefore,
P(36 ≤ x ≤ 40) = 0.66 - 0.34 = 0.32
