Question

In a certain town, the number of internet glitches per day is a normal distribution with a mean of 20 and standard deviation of 4. What is the probability that over the next 5 days, the mean number of glitches per day will be larger than 25, assuming that the given distribution remains unchanged over the next 5 days? (round your answer to the nearest thousandth)

Answer 1

Explanation:

Since the the number of internet glitches per day is a normal distribution and the the given distribution remains unchanged over the next 5 days, we would apply the formula for normal distribution which is expressed as

z = (x - u)/s

Where

x = the number of internet glitches per day.

u = mean

s = standard deviation

From the information given,

u = 20 glitches per day.

s = 4

We want to find

P(x greater than 25). It is also expressed as 1 - P(x lesser than or equal to 25)

P(x lesser than or equal to 25) =

For x = 25,

z = (25 - 20)/4 = 5/4 = 1.25

Looking at the normal distribution table, the corresponding value for the z score is 0.89435

P(x greater than 25) = 1 - 0.89435 = 0.106