Suppose that the duration of trouble-free operation of a new vacuum cleaner is normally distributed with a mean of 72 weeks and a variance of 144 weeks^2. The research department randomly selects 25 customers who bought these vacuum cleaners and records the 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).
Added by Mario R.
Step 1
Given that the variance is 144 weeks^2 and the sample size is 25, the standard error of the sample mean is calculated as: Standard Error (SE) = sqrt(variance / sample size) = sqrt(144 / 25) = 2.4 weeks Show more…
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