Susan has been on a bowling team for 14 years. after examining all of her scores over that period of time, she finds that they follow a normal distribution. her average score is 225, with a standard deviation of 13. if during a typical week susan bowls 16 games, what is the probability that her average score is more than 230? (a) 0.0620(b) 0.3520(c) 0.6480(d) 0.9382

There is a 6.18% probability that her average score is more than 230.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation , a large sample size can be approximated to a normal distribution with mean and standard deviation

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Her average score is 225, with a standard deviation of 13. This means that .

If during a typical week Susan bowls 16 games, what is the probability that her average score is more than 230?

This is 1 subtracted by the pvalue of Z when .

By the Central Limit Theorem, we have

has a pvalue of 0.9382. This means that there is a 1-0.9382 = 0.0618 = 6.18% probability that her average score is more than 230.

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step-by-step explanation: