Exam 6: Continuous Probability Distributions

The mean of a normally distributed group of weekly incomes of a large group of executives is $1,000 and the standard deviation is $100. What is the z-score for an income of $1,100?

Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years, (based on data from "Getting Things Fixed, "Consumer Reports). (i) The replacement time that separated the top 20% from the bottom 80% is 9.124 years. (ii. The probability that a randomly selected TV will be replaced in less than 4.0 years is 0.40.

Bottomline Ink, a forms managementcompany, fills 100 orders a day with a 2% error rate in the completed orders. Assume this to be a binomial distribution. What is the standard deviation for this distribution?

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

i. Asymptotic, means that the normal curve gets closer and closer to the X-axis but never actually touches it. ii. When referring to the normal probability function, there is not just one of them; there is a "family" of them. iii. Some normal probability distributions have equal arithmetic means, but their standard deviations may be different.

Which of the following is true in a normal distribution?

A new extended-life light bulb has an average service life of 750 hours, with a standard deviation of 50 hours. If the service life of these light bulbs approximates a normal distribution, about what percent of the distribution will be between 600 hours and 900 hours?

Ball-Bearings, Inc. produces ball bearings automatically on a Kronar BBX machine. For one of the ball bearings, the mean diameter is set at 20.00 mm (millimetres). The standard deviation of the production over a long period of time was computed to be 0.150 mm. What percent of the ball bearings will have diameters 20.27 mm or more?

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 1.82. (iii) The z-score of the student from section 2 is 1.87.

Assume that human body temperatures are normally distributed with a mean of 36.4 ^$\circ$ C and a standard deviation of 0.7 ^$\circ$ C. If we define a fever to be a body temperature above 38.0 ^$\circ$ C. (i) 01.1% of normal and healthy persons would be considered to have a fever. (ii. This suggests that a cut-off of 38.0 ^$\circ$ C is appropriate.

Two competitive brothers, who work in two different industries, were comparing their salaries. Because there is a difference of 4 years in their respective work experience, they decided to compare, not their actual salaries, but to compare their salaries against their company averages to see who is doing better. The following gives the brothers salaries, companies mean, and standard deviation for each company. Which brother earns a higher salary compared to the rest of their colleagues?

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 standard deviation for this distribution?

A major credit card company has determined that customers charge between $100 and $1,100 per month. Given that the average monthly amount charged is uniformly distributed, what is the probability that a person charges less than $200 per month?

Management is considering adopting a bonus system to increase production. One suggestion is to pay a bonus on the highest 5 percent of production based on past experience. Past records indicate that, on the average, 4,000 units of a small assembly are produced during a week. The distribution of the weekly production is approximately normally distributed with a standard deviation of 60 units. If the bonus is paid on the upper 5 percent of production, the bonus will be paid on how many units or more?

i. The mean of a normal distribution is represented by $\sigma$ . ii. Some normal probability distributions have equal arithmetic means, but their standard deviations may be different.

The standard normal probability distribution is one which has:

Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years, (based on data from "Getting Things Fixed, "Consumer Reports). (i) The replacement time that separated the top 20% from the bottom 80% is 9.124 years. (ii. The probability that a randomly selected TV will be replaced in less than 4.0 years is 0.00.

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.

i. The uniform probability distribution's shape is a rectangle. ii. The uniform probability distribution is symmetric about the mode. iii. In a uniform probability distribution, P(x) is constant between the distribution's minimum and maximum values.

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.