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kotykmax [81]
2 years ago
10

Some IQ tests are standardized to a Normal model N(100,19). What is the cutoff value for the top 5% of all IQs

Mathematics
1 answer:
Montano1993 [528]2 years ago
8 0

Answer:

The cutoff value for the top 5% of all IQs is 131.255.

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 = 100, \sigma = 19

What is the cutoff value for the top 5% of all IQs

This is the 100 - 5 = 95th percentile, which is X when Z has a pvalue of 0.95. So X when Z = 1.645.

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

1.645 = \frac{X - 100}{19}

X - 100 = 19*1.645

X = 131.255

The cutoff value for the top 5% of all IQs is 131.255.

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