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Dvinal [7]
3 years ago
6

Let x be a continuous random variable that follows a normal distribution with a mean of 185 and a standard deviation of 20. Find

the value of x so that the area under the normal curve to the left of x is approximately 0.8869. Round your answer to two decimal places.
Mathematics
1 answer:
andrew-mc [135]3 years ago
4 0

Answer:

x = 209.2

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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, or the area to the left of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X, which is the area to the right of X.

Mean of 185 and a standard deviation of 20.

This means that \mu = 185, \sigma = 20

Find the value of x so that the area under the normal curve to the left of x is approximately 0.8869.

This is X when Z has a p-value of 0.8869, so X when Z = 1.21.

Z = \frac{X - \mu}{\sigma}

1.21 = \frac{X - 185}{20}

X - 185 = 20*1.21

X = 209.2

So

x = 209.2

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