Question: suppose that the duration of troublefree operation of a new...

Suppose that the duration of trouble-free operation of a new vacuum cleaner is normally distributed with a mean of 72 weeks and variance of 144 weeks². The research department randomly selects 25 customers who bought these vacuum cleaners and records duration (in weeks) of trouble-free operation.

 

The standard error of the sample mean is  weeks (1 decimal place).

 

 

The probability that the average duration of trouble-free operation time is between 75 weeks and 78 weeks is  (4 decimal places).