The average life of a manufacturer’s refrigerator is 11.5 years with a standard

Question

The average life of a manufacturer’s refrigerator is 11.5 years with a standard deviation of 2.5 years. If the lives of the refrigerators are thought to be normally distributed, find a. the probability that the mean life of twelve such refrigerators is between 10 and 10.5 years, b. the value of for which 90% of random samples of twelve are greater than. The average life of a manufacturer’s refrigerator is 11.5 years with a standard deviation of 2.5 years. If the lives of the refrigerators are thought to be normally distributed, find a. the probability that the mean life of twelve such refrigerators is between 10 and 10.5 years, b. the value of for which 90% of random samples of twelve are greater than. The average life of a manufacturer’s refrigerator is 11.5 years with a standard deviation of 2.5 years. If the lives of the refrigerators are thought to be normally distributed, find a. the probability that the mean life of twelve such refrigerators is between 10 and 10.5 years, b. the value of for which 90% of random samples of twelve are greater than.

Explanation / Answer

a)

b)

for 10 percentile ; z score =-1.28

hence corresponding mean life =mean +z*std error =11.5-1.28*0.7217 =10.58 Years ~ 10.6 Years

for normal distribution z score =(X-)/ here mean=       = 11.500 std deviation   == 2.5 sample size       =n= 12 std error=x=/n= 0.7217

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