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Suppose that the duration of trouble-free operation of a new vacuum cleaner is normally distributed with...

Suppose that the duration of trouble-free operation of a new vacuum cleaner is normally distributed with mean 500 days and a standard deviation of 81 days. The research department randomly selects 36 customers who bought these vacuum cleaners and records duration (in days) of trouble-free operation. The standard error of the sample mean is days (1 decimal place). The probability that the average duration of trouble-free operation time is between 480 days and 530 days is (4 decimal places).

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