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kirill [66]
3 years ago
8

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round y

our answer to four decimal places.)
μ = 29;
σ = 3.4
P(x ≥ 30) = ______.
Mathematics
1 answer:
Anarel [89]3 years ago
4 0

Answer:

P(x ≥ 30) = 0.3859

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\mu = 29, \sigma = 3.4

This probability is going to be 1 subtracted by the pvalue of Z when X = 30. So

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

Z = \frac{30 - 29}{3.4}

Z = 0.29

Z = 0.29 has a pvalue of 0.6141

1 - 0.6141 = 0.3859

So

P(x ≥ 30) = 0.3859

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