Question

A project is found to have expected time T = 35.33 days and variance V = 3.22.

a. What value of z is needed to find the probability that the project will take at least 40 days? (round final answer to 2 decimals as needed)
b. What value of z is needed to find the probability that the project will take at most 40 days? (round final answer to 2 decimals as needed)
c. What value of z is needed to find the probability that the project will take at most 30 days? (round final answer to 2 decimals as needed)

Answer 1

a)
`z = (40-35.33)/(1.794)= 2.60`

b)
`z = (40-35.33)/(1.794)= 2.60`

c)
`z = (30-35.33)/(1.794)= -2.97`

Explanation:

For this case we know that the mean for the random variable of interest is
`\mu = 35.33` and the variance
`\sigma^2 = 3.22` so then the deviation would be
`\sigma = √(3.22)= 1.794`

The z score is given by thsi formula:

`z = (X -\mu)/(\sigma)`

Part a

We want this probability:

`P(X>40)`

And if we find the z score we got:

`z = (40-35.33)/(1.794)= 2.60`

And we can find this probability:
`P(Z>2.60)`

Part b

We want this probability:

`P(X<40)`

And if we find the z score we got:

`z = (40-35.33)/(1.794)= 2.60`

And we can find this probability:
`P(Z<2.60)`

Part c

We want this probability:

`P(X<30)`

And if we find the z score we got:

`z = (30-35.33)/(1.794)= -2.97`

And we can find this probability:
`P(Z<-2.97)`