Question

1) A manufacturer knows that their items have a normally distributed lifespan, with a mean of 14.6 years, and standard deviation of 4.8 years.

The 6% of items with the shortest lifespan will last less than how many years?

Give your answer to one decimal place.
(if possible, can answer be displayed from excel)

2) A particular fruit's weights are normally distributed, with a mean of 221 grams and a standard deviation of 12 grams.

The heaviest 6% of fruits weigh more than how many grams?

Give your answer to the nearest gram.

Answer 1

1)

X ~ N ( µ = 14.6 , σ = 4.8 )

P ( X < x ) = 6% = 0.06

To find the value of x

Looking for the probability 0.06 in standard normal table to calculate critical value Z = -1.5548

Z = ( X - µ ) / σ

-1.5548 = ( X - 14.6 ) / 4.8

Solve for X

X = 7

2)

X ~ N ( µ = 221 , σ = 12 )

P ( X > x ) = 1 - P ( X < x )

P(X < x) = 1 - 0.06

P(X < x) = 0.94

To find the value of x

Looking for the probability 0.94 in standard normal table to calculate critical value Z = 1.5548

Z = ( X - µ ) / σ

1.5548 = ( X - 221 ) / 12

X = 240