2-41 the time to complete a construction project is normally distributed with a mean of 60 weeks and a standard deviation of 4 weeks. what is the probability the project will be finished in 62 weeks or less? 62-60/4=2/4=0.5=69146 what is the probability the project will be finished in 66 weeks or less? 66-60/4=6/4=1.5 what is the probability the project will take longer than 65 weeks?

69.15% probability the project will be finished in 62 weeks or less.

93.32% probability the project will be finished in 66 weeks or less.

10.56% probability the project will take longer than 65 weeks.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

What is the probability the project will be finished in 62 weeks or less?

This is the pvalue of Z when X = 62.

has a pvalue of 0.6915.

So there is a 69.15% probability the project will be finished in 62 weeks or less.

What is the probability the project will be finished in 66 weeks or less?

This is the pvalue of Z when X = 66.

has a pvalue of 0.9332.

So there is a 93.32% probability the project will be finished in 66 weeks or less.

What is the probability the project will take longer than 65 weeks?

This is 1 subtracted by the pvalue of Z when X = 65.

has a pvalue of 0.8944.

So there is a 1-0.8944 = 0.1056 = 10.56% probability the project will take longer than 65 weeks.

d.) yes, because the volume of the cone is greater than the volume of the sphere

step-by-step explanation: