Question

1. The time it takes to assemble a car in a certain factory is normally distributed with a mean of 20 hours and a standard deviation of 2 hours. [Probability = percent]

1. What is the probability that a car can be assembled in less than 19.4 hours?
2. What is the probability that a car can be assembled between 20 and 22 hours?
3. What is the probability that it will take more than 23 hours to assemble a car?
4. What is the 70th percentile of the car assembling time?

Please show formula and Value

Answer 1

Solution :

a.

P(x < 19.4) = P[(x - ) / < (19.4 - 20) / 2]

= P(z < -0.3)

= 0.3821

Probability = 0.3821

b.

P(20 < x < 22) = P[(20 - 20)/ 2) < (x - ) /  < (22 - 20) / 2) ]

= P(0 < z < 1)

= P(z < 1) - P(z < 0)

= 0.8413 - 0.5

= 0.3413

Probability = 0.3413

c.

P(x > 23) = 1 - P(x < 23)

= 1 - P[(x - ) / < (23 - 20) / 2)

= 1 - P(z < 1.5)

= 1 - 0.9332

= 0.0668

Probability = 0.0668

d.

Using standard normal table,

P(Z < z) = 70%

P(Z < 0.52) = 0.7

z = 0.52

Using z-score formula,

x = z * +

x = 0.52 * 2 + 20 = 21.04

The 70th percentile of the car assembling time is 21.04