7. The time taken to assemble a car in a certain plant is a random variable having a normal distribution of 20 hours and a standard deviation of 2 hours. What is the probability that a car can be assembled at this plant in a period of time a) less than 19.5 hours

Answer: The probability is 0.4

Step-by-step explanation:

Since the time taken to assemble a car in a certain plant is a random variable having a normal distribution, we would apply the formula for normal distribution which is expressed as

z = (x - µ) / σ

Where

x = time taken to assemble cars

µ = mean time

σ = standard deviation

From the information given,

µ = 20 hours

σ = 2 hours

We want to find the probability that a car can be assembled at this plant in a period of time less than 19.5 hours. It is expressed as

P (x < 19.5) = 1 - P (x ≤ 19.5)

For x = 19.5

z = (19.5 - 20) / 2 = - 0.25

Looking at the normal distribution table, the probability corresponding to the z score is 0.4