Question

In: Statistics and Probability

A normally distributed population has a mean of 74 and a standard deviation of 14. Determine...

A normally distributed population has a mean of 74 and a standard deviation of 14. Determine the probability that a random sample of size 24 has an average between 71 and 80.

Round to four decimal places.

Expert Solution

Solution :

Given that,

mean = = 74

standard deviation = = 14

n=24

= 74

= / n = 14/ 24=2.86

= P(71< <80 ) = P[(71-74) /2.86 < ( - ) / < (80-74) / 2.86)]

= P(-1.05 < Z < 2.10)

= P(Z <2.10 ) - P(Z < -1.05)

Using z table,

= 0.9821 -0.1469

probability = 0.8352

orchestra answered 2 years ago

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