Acertain 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.

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