Exam 6: The Normal Probability Distribution

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. -______students earned more than $36,000?

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). -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, the probability of a pregnancy lasting 300 days or longer is_____ . The result suggests that the husband ( (is/is not) ) the father of the child.

i. The normal curve falls off smoothly in either direction from the central value. Since it is asymptotic, the curve gets closer and closer to the X-axis, but never actually touches it. ii. The mean (µ) divides the normal curve into two identical halves. Iii) The number of different normal distributions is unlimited.

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). -The probability that a randomly selected TV will be replaced in less than 4.0 years is ______.

In a standard normal distribution, µ = ____and ? =___ .

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 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 5% from the lower 95% of the incomes?

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?

015 litres. What is the probability a container will have less than 2 litres?

An analysis of the grades on the first test in History 101 revealed that they approximate a normal curve with a mean of 75 and a standard deviation of 8. The instructor wants to award the grade of A to the upper 10 percent of the test grades. What is the dividing point between an A and a B grade?

A loaf of bread is normally distributed with a mean of 22 ounces and a standard deviation of ½ ounces. -The probability that a loaf of bread is between 21.75 and 22.25 ounces is _______.

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 less than 60?

About______ percent of the area under the normal curve is within plus two and minus two standard deviation of the mean.

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. Which student scored better compared to the rest of their section?

What is the distribution with a mean of 0 and a standard deviation of 1 called?

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.

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 new drug has been developed that is found to relieve nasal congestion in 90 percent of those with the condition. The new drug is administered to 300 patients with the condition. What is the probability that more than 265 will be relieved of nasal congestion?

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?

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?