Give an example of a problem when you may need to use the central limit theorem...

Give an example of a problem when you may need to use the central limit theorem to compute thr cjances of an event and why

Expert Solution

Assume that the systolic blood pressure of 30-year-old males is normally distributed, with an average of 122 mmHg and a standard deviation of 10 mmHg.

A random sample of 16 men from this age group is selected. Calculate the probability that the average blood pressure of the sample will be greater than 125 mmHg.

The population is normally distributed, so sample means are also normally distributed for any sample size. Calculate the standard error of the mean = 10 / SQRT(16) = 2.5. Calculate the z-score for the sample mean, X Bar = 125.

So take (125-122) /2.5 = 1.2. Therefore, z=1.20 now you need to find a reference table for z.

According to normal standard table it is 0.3849. The area below the curve on each side of the mean is 0.5, and the area between
the mean and the z-score 1.20 is 0.3849. Calculate the probability that the average blood pressure of the sample will be greater than 125 mmHg: = 0.5 - 0.3849 = 0.1151 or 11.51%.

I hope this helped as a practical application.

milcah answered 1 month ago

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