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kupik [55]
3 years ago
11

Find z such that 59% of the standard normal curve lies between −z and z. (Round your answer to two decimal places.)

Mathematics
1 answer:
victus00 [196]3 years ago
4 0

Answer:

Z = 0.82

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.

Find z such that 59% of the standard normal curve lies between −z and z.

The normal distribution is symmetric, which means that this is:

From the 50 - (59/2) = 20.5th percentile

To the 50 + (59/2) = 79.5th percentile.

The 20.5th percentile is -Z and the 79.5th percentile is Z.

79.5th percentile

Z with a pvalue of 0.795.

Looking at the z-table, it is Z = 0.824.

Rounding to two decial places, the answer is Z = 0.82.

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2 years ago
In Pennsylvania the average IQ score is 101.5. The variable is normally distributed, and the population standard deviation is 15
blsea [12.9K]

Answer:

We conclude that the Pennsylvania school district have an IQ higher than the average of 101.5

Step-by-step explanation:

We are given the following in the question:

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Sample size, n = 30

Alpha, α = 0.05

Population standard deviation, σ = 15

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We use one-tailed z test to perform this hypothesis.

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z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }

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