Question

The task of framing a building has been estimated to take anaverage of 25 days with astandard deviation of 4 days. What duration should be used if there is to be a 90%confidence that the duration will not be exceeded?

Answer 1

30.128 days

Step-by-step explanation:

Given that:

Mean = 25

Standard deviation = 4

Confidence interval = 90% = 0.9

Since the confidence interval should not exceed 90%

Then using z test table

P(z) = 0.9

For 0.8997 , we get = 1.28

For 0.9015, we get = 1.29

∴

`(0.9 - 0.8897)/(0.9015 - 0.8997 )=( z - 1.28)/(1.29 -1.28)`

By solving

Z = 1.282

Thus, the duration to be used so that it will not exceed 90% C.I is:

Z = (x - μ)/σ

1.282= ( x - 25)/4

1.282 * 4 = x - 25

(1.282*4)+25 = x

x = 30.128 days