Question

The lifespan of a car battery is approximately normally distributed, with mean equivalent to 4 years and a standard deviation of 5 years. What is the probability that a random sample of 25 car batteries would have an expected lifespan of (i) more than 6 years? (ii) at least 3 years but less than 7 years?

Answer 1

(i) $P(X>6)=P(Z>\frac{6-4}{\frac{5}{\sqrt{25}}})=P(Z>2)=0.0228.$

(ii) $P(3<X<7)=P(\frac{3-4}{\frac{5}{\sqrt{25}}}<Z<\frac{7-4}{\frac{5}{\sqrt{25}}})=P(-1<Z<3)=$

$=P(Z<3)-P(Z<-1)=0.8400.$