The probability that a rental car will be stolen is 0.001. if 25,000 cars are rented from hertz, what is the normal approximation to the probability that fewer than 20 will be stolen?

N=25000, p=0.001, np=25000*0.001=25 >10, so the normal approximation should apply.

fewer than 20 = > 0,1,2,3 ... 19

Applying the continuity correction, we have X<19.5.

μ =np=25

σ ²=npq=25000*.001*.999=24.975 = >

σ =√ (24.975) = 4.9975

Z (X<19.5) = (19.5-25) / 4.9975=-1.100550

P (X<19.5) = P (Z<-1.10055) = 0.1355463 [from normal probability table, left tail]

Hence normal approximation to probability that fewer than 20 cars will be stolen is 0.1355.

[actual value by binomial distribution is 0.133450. approximation is quite close]