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

###### Question details

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 weeks^{2}. 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).