Question

Company XYZ know that replacement times for the DVD players it produces are normally distributed with a mean of 9.7 years and a standard deviation of 2.1 years. Find the probability that a randomly selected DVD player will have a replacement time less than 5.9 years? P(X < 5.9 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.

If the company wants to provide a warranty so that only 3.3% of the DVD players will be replaced before the warranty expires, what is the time length of the warranty? warranty = years

If you could tell me what equation to put in EXEL that would be great. My professor only wants us to use exel.

Answer 1

μ = 9.7, σ = 2.1

(a) x = 5.9

z = (x - μ)/σ = (5.9 - 9.7)/2.1 = -1.8095

P(x < 5.9) = P(z < -1.8095) = 0.0352

(b) Area under the standard normal curve is 3.3% (that is 0.033) to the left of z = -1.8384

x = μ + z * σ = 9.7 - 1.8384 * 2.1 = 5.8394 (6 years)