# [高中數學]英文版Data Analysis

A manufacturer of electric motors claims that the life time of its motors is normally distributed around a mean of 60,000 hours with a standard deviation of 2500 hours.

a) What percentage of the motors would you expect to last less than 52,500 hours?

b) What percentage of the motors would you expect to last longer than 65,000 hours?

c) Out of a sample of 4000 motors, how many motors should last longer than 55,000 hours?

d) The motor that I bought fried out after 64,125 hours. What is the Z-score for particular motor? What is the area under the normal distribution curve for all z-scores lower than the value you calculated?

Rating

A manufacturer of electric motors claims that the life time of its motors is normally distributed around a mean of 60,000 hours with a standard deviation of 2500 hours.

a) What percentage of the motors would you expect to last less than 52,500 hours?

P(X<52,500) = P(Z<-3) = 0.1350%

(查常態分配表，或利用Excel函數功能"=NORMSDIST(-3)")

b) What percentage of the motors would you expect to last longer than 65,000 hours?

P(X>65,000) = P(Z>2) = 2.2750%

(查常態分配表，或利用Excel函數功能"=1-NORMSDIST(2)")

c) Out of a sample of 4000 motors, how many motors should last longer than 55,000 hours?

P(X>55,000) = P(Z>-2) = 97.7250%

4,000*97.7250% = 3,909

d) The motor that I bought fried out after 64,125 hours. What is the Z-score for particular motor? What is the area under the normal distribution curve for all z-scores lower than the value you calculated?

Z-score = (64,125-60,000) / 2,500 = 1.65

P(Z<1.65) = 95.0529%