Exam 6: The Normal Probability Distribution

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 a "C" on the test, a student must be in the top 25% of the class. What should a student score to receive a "C"?

An accelerated life test on a large number of type-D alkaline batteries revealed that the mean life for a particular use before they failed is 19.0 hours. The distribution of the lives approximated a normal distribution. The standard deviation of the distribution was 1.2 hours. About 95.44 percent of the batteries failed between what two values?

i. In terms of a formula the standardized value of z is found by z = (X - µ)/σ. ii. The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of less than 10. iii. A computed z for X values to the left of the mean is positive.

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.

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

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.

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?

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?

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

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 different arithmetic means and different standard deviations.

The shape of any uniform probability distribution is

Suppose a tire manufacturer wants to set a mileage guarantee on its new XB 70 tire. Life test revealed that the mean mileage is 47,900 and the standard deviation of the normally distributed distribution of mileage is 2,050 miles. The manufacturer wants to set the guaranteed mileage so that no more than 5 percent of the tires will have to be replaced. What guaranteed mileage should the manufacturer Announce?

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 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 between $20,000 and $40,000?

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?

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 22.25 ounces is ______.

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.

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 mean for this distribution?

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 after more than 10.0 years is______