Question

The life spans of car batteries are normally distributed, with a mean of 62 months and...

The life spans of car batteries are normally distributed, with a mean of 62 months and a standard deviation of 5 months.

(a) Find the probability that the life span of a randomly selected battery is less than 42 months.

(b) Find the probability that the life span of a randomly selected battery is between 44 and 56 months.

(c) What is the shortest life expectancy a car battery can have and still be in the top 5% of life expectancies?

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Answer #1

= 62 and Given: fu σ= a)When,x-42 -4 p(x < 42)=p(2 < -4 )-| 0.0000| By standard normal table (negative values)b)When,x:44 -=-μ = -3.6 p(x 44) P(Z< -3.60.0002 By standard normal table (negative values) When,x- 56 Z1.2 p(x < 56)=Plz<-1.2 )-| 0.1151|By standard normal table (negative values) The required probability is p 44 x< 56 ) (-3.6 <z< -1.2) =p(z < -1.2).p (z<-3.6) 0.1151~ 0.0002 0.1149c)The z score corresponding to the area 0.95 is z 1.64 By standard normal table Now we use X-11+ZƠ x- 70.2 i.e; 70 months

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