Exam 6: Continuous Probability Distributions

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 have a net loss is:

A loaf of bread is normally distributed with a mean of 22 ounces and a standard deviation of ½ ounces. (i) The probability that a loaf of bread is > 23 ounces is 0.0228. (ii. The probability that a loaf of bread is > 21 ounces is 0.9772. (iii) The probability that a loaf of bread is < 24 ounces is 1.0.

The mean amount of gasoline and services charged by Key Refining Company credit customers is $70 per month. The distribution of amounts spent is approximately normal with a standard deviation of $10. What is the probability of selecting a credit card customer at random and finding the customer charged between $70 and $83?

i. The total area within any continuous probability distribution is equal to 1.00. ii. For any continuous probability distribution, the probability, P(x), of any value of the random variable, X, can be computed. iii. For any discrete probability distribution, the probability, P(x), of any value of the random variable, X, can be computed.

Determine the z-score associated with an area of 0.25 from the mean of a normal distribution to that positive z-score.

What is the value of the continuity correction factor?

Two business major students, in two different sections of economics, were comparing test scores. The following gives the students' scores, class mean, and standard deviation for each section. (i) The student from Section 2 scored better compared to the rest of their section. (ii. The z-score of the student from section 1 is 1.28. (iii) The z-score of the student from section 2 is 1.87.

What is an important similarity between the uniform and normal probability distributions?

The annual commissions per salesperson employed by a manufacturer of light machinery averaged $40,000 with a standard deviation of $5,000. What percent of the sales persons earn between $32,000 and $42,000?

A loaf of bread is normally distributed with a mean of 22 ounces and a standard deviation of ½ ounce. (i) The probability that a loaf of bread is < 20 ounces is 0.0. (ii. The probability that a loaf of bread is > 21 ounces is 0.9772. (iii) The probability that a loaf of bread is < 24 ounces is 1.0.

A random variable from an experiment where outcomes are normally distributed can have

Two normal distributions are compared. One has a mean of 10 and a standard deviation of 10. The second normal distribution has a mean of 10 and a standard deviation of 2. Which of the following is true?

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?

Determine the z-score associated with an area of.1950 from the mean of a normal distribution to that positive z-score.

The seasonal output of a new experimental strain of pepper plants was carefully weighed. The mean weight per plant is 15.0 pounds, and the standard deviation of the normally distributed weights is 1.75 pounds. Of the 200 plants in the experiment, how many produced peppers weighing between 13 and 16 pounds?

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. What is the income that separates the top 25% from the lower 75% of the incomes?

i. The uniform probability distribution's standard deviation is proportional to the distribution's range. ii. The uniform probability distribution is symmetric about the mode. iii. For a uniform probability distribution, the probability of any event is equal to 1/(b - a).

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. 314 students earned between $27,000 and $33,000. (iii) 239 students earned between $24,000 and $30,000.

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 greater than 65?

Which of the following is NOT a characteristic of the normal probability distribution?