Mathematics, 27.01.2020 23:31 shikiaanthony

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?

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Answer from: kalbaugh

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 $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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:

$\mu = 60, \sigma = 4$

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

This is the pvalue of Z when X = 62.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{62 - 60}{4}$

Z = 0.5

Z = 0.5 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.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{66 - 60}{4}$

Z = 1.5

Z = 1.5 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.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{65 - 60}{4}$

Z = 1.25

Z = 1.25 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.

Answer from: Quest

answer: 230 miles ( vote ! )

step-by-step explanation:

180.39 minus 17.99 equals 162.4

then divide 162.4 by .80 to get 230

Answer from: Quest

f(x) is the value of the function. b is the value of the function when x equals zero or the y-coordinate of the point where the line crosses the y-axis in the coordinate plane.

step-by-step explanation:

hope this !

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2-41 the time to complete a construction project is normally distributed with a mean of 60 weeks and...