Exam 6: Continuous Probability Distributions

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 between 20.75 and 23.25 ounces is 0.9876. (ii. The probability that a loaf of bread is > 21 ounces is 0.9772.

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 probability that there will be more than 5 order errors in a given day?

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. What is the z-score of Andy's salary?

(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 1.

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

(i. The mean of a normal probability distribution is 60 and the standard deviation is 5. 95.44 percent of observations lie between 50 and 60. (ii) A z-value of -2.00 indicates that corresponding X value lies to the left of the mean. (iii) One of the properties of the normal curve is that it gets closer to the horizontal axis, but never touches it. This property of the normal curve is called asymptotic.

A statistics student receives a grade of 90 on a statistics midterm. If the corresponding z-score equals +1.5 and the standard deviation equals 7, determine the average grade on this exam.

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 22.25 ounces is 0.0. (ii. The probability that a loaf of bread is between 21.75 and 22.25 ounces is 0.3830. (iii) The probability that a loaf of bread is < 24 ounces is 1.0.

(i. About 95.5% percent of the area under the normal curve is within plus two and minus two standard deviations of the mean. (ii) The normal distribution is a continuous probability distribution. (iii) In a standard normal distribution, µ = 0 and $\sigma$ = 1.

i. A z-score is the distance between a selected value (X)and the population mean ( $\mu$ ) divided by the population standard deviation ( $\sigma$ ). 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 negative.

What is the area under the normal curve between z = -1.0 and z = -2.0?

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. What is the z-score of Tom's salary?

The employees of Cartwright Manufacturing are awarded efficiency ratings. The distribution of the ratings approximates a normal distribution. The mean is 400, the standard deviation 50. What is the area under the normal curve between 400 and 482?

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 mean for this distribution?

The mean of a normal distribution is 400 kg. The standard deviation is 10 kg. What is the area between 415 kg and the mean of 400 kg?

From past history, the scores on a statistics test are normally distributed with a mean of 70% and a standard deviation of 5%. To earn an "A" on the test, a student must be in the top 5% of the class. What should a student score to receive an "A"?

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 < 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 0.00.

(i. The mean of a normal probability distribution is 60 and the standard deviation is 5. 95.44 percent of observations lie between 50 and 70. (ii) A z-value of -2.00 indicates that corresponding X value lies to the left of the mean. (iii) One of the properties of the normal curve is that it gets closer to the horizontal axis, but never touches it. This property of the normal curve is called asymptotic.

A study of a company's practice regarding the payment of invoices revealed that on the average an invoice was paid 20 days after it was received. The standard deviation equaled five days. Assuming that the distribution is normal, what percent of the invoices were paid within 15 days of receipt?

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 more than $55,000?