Question

1. In testing a certain kind of truck over rugged terrain, it is found that overall 20% of the trucks fail to complete the test run. For the next 5 trucks to be tested, find the probability that 3 trucks will fail.
2. Assume the life of a certain light bulb is normally distributed with a mean of 12 months and a standard deviation of 3 months. What is the probability that the lifetime of a given light bulb is longer than 15 months?

Answer 1

Given that ,

p = 0.20

1 - p = 1 - 0.20= 0.80

n =5

Using binomial probability formula ,

P(X = x) = (n C x) * px * (1 - p)n - x

P(X = 3) = (5 C 3) * 0.203 * (0.80)2

probability =0.0512

(B)

Solution :

Given that,

mean = = 12

standard deviation = = 3

P(x >15 ) = 1 - P(x<15 )

= 1 - P[(x -) / < (15-12) /3 ]

= 1 - P(z <1 )

Using z table

= 1 - 0.8413

probability= 0.1587