1) A population of values has a normaldistribution with ? = 97.3 and ? = 21.5 .
You intend to draw a random sample of size n = 42 .
A) Find the probability that a single randomlyselected value is greater than 107.3. P(X > 107.3) =
Round to 4 decimal places.
B) Find the probability that the sample mean isgreater than 107.3. P( ¯¯¯ X > 107.3) =
Round to 4 decimal places.
Answers obtained using exact z-scores or z-scores rounded to 2decimal places are accepted.
2) Company XYZ know that replacement times forthe quartz time pieces it produces are normally distributed with amean of 11.3 years and a standard deviation of 1 years.
A) Find the probability that a randomlyselected quartz time piece will have a replacement time less than8.7 years? P(X < 8.7 years) = Enter your answer accurateto 4 decimal places.
Answers obtained using exact z-scores or z-scores rounded to 3decimal places are accepted.
B) If the company wants to provide a warrantyso that only 1.5% of the quartz time pieces will be replaced beforethe warranty expires, what is the time length of the warranty?
warranty = years Enter your answer as a number accurateto 1 decimal place.
Answers obtained using exact z-scores or z-scores rounded to 3decimal places are accepted.
