Question

1) A population of values has a normal distribution with μ = 97.3 and σ = 21.5 .

You intend to draw a random sample of size n = 42 .

A) Find the probability that a single randomly selected value is greater than 107.3. P(X > 107.3) =

Round to 4 decimal places.

B) Find the probability that the sample mean is greater than 107.3. P( ¯¯¯ X > 107.3) =

Round to 4 decimal places.

Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted.

2) Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 11.3 years and a standard deviation of 1 years.

A) Find the probability that a randomly selected quartz time piece will have a replacement time less than 8.7 years? P(X < 8.7 years) = Enter your answer accurate to 4 decimal places.

Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

B) If the company wants to provide a warranty so that only 1.5% of the quartz time pieces will be replaced before the warranty expires, what is the time length of the warranty?

warranty = years Enter your answer as a number accurate to 1 decimal place.

Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

1. a)

b)

2. a)

b)