Answer:
The answers are as follows
(a) 0.5793
(b) 0.4207
(c) 0.5793
(d) 177.9 minutes.
Explanation:
Given,
Average = 168 minutes. Average is called as mean.
So, mean(m) = 168
standard deviation(sd) = 10
Using the formula, Z = (X - m)/(sd)
(a) here X = 170
so, Z = (170 - 168)/(10) => 2/10 => 0.2
It was asked to find the probability that a randomly selected game will be completed in less than 170 minutes.
it implies X < 170 => Z < 0.2
P(X < 170) = P(Z < 0.2) = 0.5793 from Z table.
(b) here X = 170
so, Z = (170 - 168)/(10) => 2/10 => 0.2
It was asked to find the probability that a randomly selected game will be completed in more than 170 minutes.
it implies X > 170 => Z > 0.2
P(X > 170) = P(Z > 0.2) = 1 - 0.5793 = 0.4207 from Z table.
(c) here X = 170
so, Z = (170 - 168)/(10) => 2/10 => 0.2
It was asked to find the probability that a randomly selected game will be completed in less than 170 minutes.
it implies X = 170 => Z = 0.2
P(X = 170) = P(Z = 0.2) = 0.5793 from Z table.
(d) Here Probability = 99% = 0.99
P(Z) = 0.99
Substituting the values in Z = (X - m)/(sd) and finding X
0.99 = (X - 168)/(10) => 9.9 = (X - 168) => X = 177.9
Therefore, the completion time in which 99% of the games will be finished is 177.9 minutes.
