Exam 6: Continuous Probability Distributions

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. 500 students earned between $20,000 and $40,000. (iii) 6 students earned less than $22,500.

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 weights of cans of fruit are normally distributed with a mean of 1,000 grams and a standard deviation of 50 grams. What percent of the cans weigh 860 grams or less?

i. Areas within a continuous probability distribution represent probabilities. ii. The Empirical Rule of probability can be applied to the uniform probability distribution. iii. The total area within a continuous probability distribution is equal to 100.

For a standard normal distribution, what is the probability that z is greater than 1.75?

The upper and lower limits of a uniform probability distribution are

The distribution of the annual incomes of a group of middle management employees approximated a normal distribution with a mean of $37,200 and a standard deviation of $800. About 68 percent of the incomes lie between what two incomes?

Which of the following is NOT true regarding the normal distribution?

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 308 days or longer is 0.0038. (ii. The result suggests that the husband is not the father of the child.

(i. The formula to convert any normal distribution to the standard normal distribution is z = (X - µ)/ $\sigma$ (ii) The standardized z value measures distance from the mean in units of standard deviation. (iii) The area under a normal curve to the right of a z-score of -1.0 is a proportion of 0.3413.

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 more than 45 of the voters from your sample voted in favour of strike action?

(i. The formula to convert any normal distribution to the standard normal distribution is z = (X - µ)/ $\sigma$ (ii) The standardized value measures distance from the mean in units of standard deviation. (iii) The area under a normal curve to the right of a z-score of zero is a proportion of 0.50.

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?

The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. Assuming a normal distribution, approximately how many scored 90 or higher?

i. In a uniform probability distribution, P(x) is constant between the distribution's minimum and maximum values. ii. For a uniform probability distribution, the probability of any event is equal to 1/(b-a). iii. The uniform probability distribution is symmetric about the mode.

i. In terms of a formula the standardized value of z is found by z = (X - µ)/ $\sigma$ . ii. The standard normal distribution is a special normal distribution with a mean of 0 and a standard deviation of 1. iii. A computed z for X values to the right of the mean is positive.

A sample of 500 evening students revealed that their annual incomes were normally distributed with a mean income of $50,000 and a standard deviation of $4,000. How many students earned between $45,000 and $53,000?

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.

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 100%. iii. The mean of a normal probability distribution is 500 and the standard deviation is 10. About 95 percent of the observations lie between 480 and 520.