QUESTION 8 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).