Exam 6: Discrete Probability Distributions

The driver's seat in most vehicles is set to comfortably fit a person who is at least 159 cm tall. The Distribution of heights of adult women is approximately normal with a mean of 161.5 cm and a Standard deviation of 6.3 cm. Determine the percentage of women who can be expected to be Uncomfortable in the driver's seat of their car without some sort of an adjustment.

i. A continuity correction compensates for estimating a discrete distribution with a continuous Distribution. ii. The normal probability distribution is generally deemed a good approximation for the binomial Probability distribution when np and n(1 - p) are both greater than five. iii. When a continuity correction factor is used, its value is 0.5.

Normally distributed observations such as a person's weight, height or shoe size occur quite Frequently in nature. Business people who are aware of this use it to their advantage. A purchasing Agent for a college bookstore buying 300 golf shirts used the normal curve to decide on the order Quantities for the various sizes. If men's average shirt size is 15.5 with a standard deviation of .50, How many shirts should be ordered in sizes over 16.5?

i. For any uniform probability distribution, the mean and standard deviation can be computed by Knowing the maximum and minimum values of the random variable. ii. In a uniform probability distribution, P(x) is constant between the distribution's minimum and Maximum values. iii. The uniform probability distribution's shape is a rectangle.

Tabulation of a strike vote showed that 90% of those voting cast their ballot in favour of strike Action. You take a sample of 50 voters. Assume this to be a binomial distribution. What is the probability that fewer than 40 of your sample voters are in favour of strike action?

i. A continuity correction compensates for estimating a discrete distribution with a continuous Distribution. ii. The binomial can be used to approximate the normal distribution for small sized samples. iii. The binomial may be used to approximate the normal distribution when the probability, p, Remains the same from trial to trial.

A national manufacturer of unattached garages discovered that the distribution of the lengths of Time it takes two construction workers to erect the Red Barn model is approximately normally Distributed with a mean of 32 hours and a standard deviation of 2 hours. What percent of the Garages take between 32 and 34 hours to erect?

The net profit from a certain investment is normally distributed with a mean of $10,000 and a Standard deviation of $5,000. The probability that the investor will not have a net loss is:

Determine the z-score associated with an area of 0.48 from the mean of a normal distribution to that Positive z-score.

i. The Empirical Rule of probability can be applied to the uniform probability distribution. ii. Areas within a continuous probability distribution represent probabilities. iii. The total area within a continuous probability distribution is equal to 1.

The mean amount spent by a family of four on food per month is $500 with a standard deviation of $75. Assuming that the food costs are normally distributed, what is the probability that a family spends less than $410 per month?

A financial advising company has determined that the price-to-earnings ratios for 20 randomly Selected publicly traded companies range between 0.9 and 2.9. Given that the price-to-earnings Ratios are uniformly distributed, what is the average price-to-earnings ratio?

i. For a normal probability distribution, about 95 percent of the area under normal curve is within Plus and minus two standard deviations of the mean and practically all (99.73 percent) of the area Under the normal curve is within three standard deviations of the mean. ii. The total area under the normal curve is 1. iii. The mean of a normal probability distribution is 500 and the standard deviation is 10. About 68 Percent of the observations lie between 480 and 520.

The shape of any uniform probability distribution is

i. Disaster Airlines determined that the mean number of passengers per flight is 152 with a standard Deviation of ten passengers. Practically all flights have between 142 and 162 passengers. ii. The total area under the normal curve is less than 1. iii. The mean of a normal probability distribution is 500 and the standard deviation is 10. About 68 percent of the observations lie between 480 and 520.

A sample of 500 evening students revealed that their annual incomes from employment in industry During the day were normally distributed with a mean income of $30,000 and a standard deviation Of $3,000. (i. 250 students earned more than $30,000. (ii. 341 students earned between $27,000 and $33,000. (iii) 239 students earned between $24,000 and $30,000.

For the standard normal distribution, what z-score corresponds with the 85% percentile?

A financial advising company has determined that the price-to-earnings ratios for 20 randomly Selected publicly traded companies range between 0.9 and 2.9. Given that the price-to-earnings Ratios are uniformly distributed, what percent of price-to-earnings ratios are between 1.90 and 2.48?

The weekly mean income of a group of executives is $1,000 and the standard deviation of this Group is $100. The distribution is normal. What percent of the executives have an income of $925 or Less?

One classic use of the normal distribution is inspired by a letter to Dear Abbey in which a wife Claimed to have given birth 308 days after a brief visit from her husband, who was serving in the Navy. The lengths of pregnancies are normally distributed with a mean of 268 days and a standard Deviation of 15 days. Given this information. (i. the probability of a pregnancy lasting 300 days or longer is 0.0166. (ii. The result suggests that the husband is the father of the child.