Question

Consider the probability that fewer than 15 out of 149 people have been in a car accident. Assume the probability that a given person has been in a car accident is 11% Approximate the probability using the normal distribution. Round your answer to four decimal places.

Answer 1

We have here , n = 149 and p = 0.11

$\mu=np=149*0.11=16.39$

$\sigma=\sqrt{n*p*(1-p)}=\sqrt{149*0.11*(1-0.11)}=3.82$

P[X<15]

=P[X<14.5]................................by using continuity correction.

$=P[Z<\frac{14.5-16.39}{3.82}]$

=P[Z<-0.495]

=0.3103............................by using Z table or by using Excel command =NORMSDIST(-0.495)