Suppose a random sample of n = 16 observations is selected from a population tha

Question

Suppose a random sample of n = 16 observations is selected from a population that is normally distributed with mean equal to 106 and standard deviation equal to 11. (a) Give the mean and the standard deviation of the sampling distribution of the sample mean x. (Enter your standard deviation to two decimal places.) mean 106 standard deviation 2.75 (b) Find the probability that x exceeds 113. (Round your answer to four decimal places.) .0054 (c) Find the probability that the sample mean deviates from the population mean mu = 106 by no more than 5. (Round your answer to four decimal places.)

Explanation / Answer

Solution:-

  c) using the standard deviation for the sampling distribution:

P( xbar > 106) = P ( z > ( 111 - 106)/2.75)

= P( z > 5/2.75)

= P( z > 1.8181)

= 0.0344

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