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Akimi4 [234]
3 years ago
10

The length of time needed to complete a certain test is normally distributed with mean 46 minutes and standard deviation 6 minut

es. Find the probability that it will take less than 37 minutes to complete the test.
Mathematics
1 answer:
madam [21]3 years ago
3 0

Answer:

0.0668 or 6.68%

Step-by-step explanation:

Mean time (μ)= 46 minutes

Standard deviation (σ) = 6 minutes

The z-score for any given time X is determined by:

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

For X = 37:

z=\frac{37-46}{6}\\ z=-1.5

A z-score of -1.5 corresponds to the 6.68th percentile of a normal distribution. The probability that it will take less than 37 minutes to complete the test is

P(X\leq 37) = 0.0668=6.68\%

The probability is 0.0668 or 6.68%

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Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 12. Use the empirical rule t
MissTica

Answer:

A) 99.7% of people have an IQ between 64 and 136.

B) 5% of people have an IQ score less than 76 or greater than 124.

C) 16% of people have an IQ score greater than 112.

Step-by-step explanation:

The Empirical Rule tells us that, in a normal or 'bell-shaped' distribution, 68% of the data is one standard deviation from the mean, 95% of the data is two standard deviations from the mean, and 99.7% of the data is three standard deviations from the mean.

A) 64 and 136 are 3 standard deviations away from the mean, so 99.7% of people have an IQ between 64 and 136.

B) 76 and 124 are 2 standard devations away from the mean, but the answer is asking what percentage is not between them. 100% - 95% gives us 5%.

C) 112 is one standard deviation away from the mean. If we want to find the percentage greater, then we can do 100% - 50% (as 112 is to the left of the mean), then we can take half of 68 to get 34%, and after subtracting 50% and 34% from the 100%, we get 16%.

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