Question

8. The average life of a refrigerator has a normal distribution with mean 14 years and standard deviation ? years. (a) If 95% of fridges last between 9 and 19 years, show that ? = 2.55 (3 s.f.). (b) What is the probability a fridge lasts less than 11 years? (c) A company guarantees fridges and will replace a refrigerator which breaks while under guarantee with a new one. The company does not want to replace more than 5% of fridges. For how long should the guarantee be made?

          8. The average life of a refrigerator has a normal distribution with mean 14 years and standard deviation ? years.

(a) If 95% of fridges last between 9 and 19 years, show that ? = 2.55 (3 s.f.).
(b) What is the probability a fridge lasts less than 11 years?
(c) A company guarantees fridges and will replace a refrigerator which breaks while under guarantee with a new one. The company does not want to replace more than 5% of fridges. For how long should the guarantee be made?

8. The average life of a refrigerator has a normal distribution with mean 14 years and standard deviation ? years.

(a) If 95% of fridges last between 9 and 19 years, show that ? = 2.55 (3 s.f.).
(b) What is the probability a fridge lasts less than 11 years?
(c) A company guarantees fridges and will replace a refrigerator which breaks while under guarantee with a new one. The company does not want to replace more than 5% of fridges. For how long should the guarantee be made?

Added by Tyler R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Joanna Quigley

03/24/2023

Step 1

We are also given that 95% of fridges last between 9 and 19 years. We can use the z-score formula to find the standard deviation: z = (X - μ) / σ For the lower bound (9 years), the z-score is -1.96 (since 95% of the data lies within ±1.96 standard deviations Show more…

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8. The average life of a refrigerator has a normal distribution with mean 14 years and standard deviation σ years. (a) If 95% of fridges last between 9 and 19 years, show that σ = 2.55 (3 s.f.). (b) What is the probability a fridge lasts less than 11 years? (c) A company guarantees fridges and will replace a refrigerator which breaks while under guarantee with a new one. The company does not want to replace more than 5% of fridges. For how long should the guarantee be made?