Question

A instrument is set to cut carpets with a mean of 68inches and standard devistion of 0.44inches. After being cut, all carpets are measured. The longest 5% of carpets must be dragged and manually trimmed to the correct length. what it the longest a carpet can be without having to be manually cut?

A. 67.12 inches

B. 67.28 inches

C. 67.34 inches

D. 68.66 inches

E. 68.72 inches

F. 68.86 inches

G. 68.88 inches

H. 69.02 inches

I. None of the other answers is correct

Answer 1

Mean = 68 inches

Standard deviation = 0.44 inches

We need to find the longest 5%

let x be the length

P[ X > x ] = 5%

P[ X > x ] = 0.05

P[ ( X - mean )/ Standard deviation > ( x - mean )/ Standard deviation ] = 0.05

P[ ( X - 68 )/ 0.44 > ( x - 68 )/ 0.44 ] = 0.05

P[ Z > ( x - 68 )/ 0.44 ] = 0.05

Also,

P[ Z > 1.645 ] = 0.05

Comparing

( x - 68 )/ 0.44 = 1.645

x - 68 = 0.44*1.645

x - 68 = 0.7238

x = 68 + 0.7238

x = 68.7238

x = 68.72 inches

P[ X > 68.72 ] = 5%

E. 68.72 inches