# Probability Distributions - Scores

See the attached file.

1. The scores for an IQ test are normally distributed with a mean of 100 and a standard deviation of 15. If a person is selected at random, what is the probability that his IQ score will fall below 105 and will it be between 90 and 110.

2. An advertising company plans to market a product for low income families. A study states that for a particular area, the average income per family is 24, 596 and the standard deviation is 6256.

a. What is the probability that the families income will be above 25,000

b. If the company plans to target the bottom 18% of the families based on income, find the cutoff scores.

3. A sample of 50 days showed that fast food restaurant served an average of 182 customers during lunch time. The standard deviation of the sample was 8. Find the 95% confidence interval for the true mean.

4. In a certain state, a survey of 500 workers showed that 45% belong to a union. Find the 90% confidence interval of the true proportion of workers who belong to a union.

5. The college president asks a teacher to estimate the average age of the students at the end of college. How large a sample is necessary if the teacher decides the estimation should be within one year and be 99% confident. The standard deviation is 4 years.

Â© BrainMass Inc. brainmass.com March 4, 2021, 7:49 pm ad1c9bdddfhttps://brainmass.com/statistics/quantative-analysis-of-data/probability-distributions-scores-125879

#### Solution Preview

Please see the attached file.

1. The scores for an IQ test are normally distributed with a mean of 100 and a

standard deviation of 15. If a person is selected at random, what is the probability

that his IQ score will fall below 105 and will it be between 90 and 110.

P(X < 105) = P(Z < 63.04%

P(90<X<110) = P(Z < ...

#### Solution Summary

This solution answers 5 probability distribution questions, addressing confidence intervals, standard deviations, probability and statistics.