Question

A certain flight arrives on time 9090 percent of the time. suppose 116116 flights are randomly selected. use the normal approximation to the binomial to approximate the probability that ?(a) exactly 9898 flights are on time. ?(b) at least 9898 flights are on time. ?(c) fewer than 100100 flights are on time. ?(d) between 100100 and 106106?, inclusive are on time.

Answer 1

Z- score is a statistical tool that is used to determine the probability of finding a number or a value under a normal distribution plot. A normal distribution assumes that the mean is equal to zero and that the standard deviation is equal to 1.  The expression to find the z score is z = (x -∪)/∅ where ∪ is the mean and ∅ is the standard deviation. 

a. p= (98/116)* 0.90 = 0.76
b. x > 98 then we use z-score, wbut find first standard dev, ∅ 
∅ = 116 * 0.90 *(1-0.90) = 10.44
z = (98- 116*0.90)/10.44 = -0.613
p = 0.73
c. x<100
z = (100- 116*0.90)/10.44 = -0.42
p=0.66
d. p = 0.73-0.66 =0.07