The time a student sleeps per night has a distribution with mean 6.15 hours and a...

The time a student sleeps per night has a distribution with mean 6.15 hours and a standard deviation of 0.5 hours. Find the probability that average sleeping time for a randomly selected sample of 40 students is more than 6.29 hours per night. Answer: (keep 4 decimal places)

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Expert Solution

Solution :

mean = = 6.15

standard deviation = = 0.5

n = 40

= = 6.15

= / n = 0.5 / 40 = 0.079

P( > 6.29) = 1 - P( < 6.29)

= 1 - P[( - ) / < (6.29 - 6.15) / 0.079 ]

= 1 - P(z < 1.77)

Using z table,

= 1 - 0.9616

= 0.0384

orchestra answered 1 year ago

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