Exam 7: Continuous Probability Distributions

The weight of cans of fruit is 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?

A major credit card company has determined that customers charge between $100 and $1100 per month. If the monthly amount charged is uniformly distributed, the standard deviation of the monthly amount charged would be ________.

A normally distributed random variable has _________.

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the probability that a flight is more than 140 minutes?

The weight of a bag of corn chips is normally distributed with a mean of 22 ounces and a standard deviation of 0.5 ounces. The probability that a bag of corn chips weighs more than 21 ounces is ____.

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

A sample of 500 part-time students revealed that their annual incomes were normally distributed with a mean income of $30,000 and a standard deviation of $3,000. The number of students who earned more than $36,000 was ______.

Management is considering a bonus system to increase production. One suggestion is to pay a bonus on the highest 5% of production based on past experience. Past records indicate that an average of 4,000 units of a small assembly is 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% of production, the bonus will be paid on how many units or more?

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the probability that a flight is between 125 and 140 minutes?

Non-stop Airlines determined that the mean number of passengers per flight is 152 with a standard deviation of 10 passengers. Practically all flights have between 142 and 162 passengers.

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 (millimeters). 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 of 20.27 mm or more?

A major credit card company has determined that customers charge between $100 and $1,100 per month. If the average monthly amount charged is uniformly distributed, the third quartile of the distribution would be _______.

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the distribution's mean?

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% of the test grades. To the nearest percent, what is the dividing point between an A and a B grade?

For the standard normal distribution, the z score that corresponds with the 85^th percentile is ________.

For normally distributed random variables, the _________ makes probability statements based on specific values of the standard deviation.

In a graph of the uniform distribution, probabilities are represented by ___________.

The weight of a bag of corn chips is normally distributed with a mean of 22 ounces and a standard deviation of 0.5 ounces. The probability that a bag of corn chips weighs between 20.75 and 23.25 ounces is ____.

The mean of a normal probability distribution is 60 and the standard deviation is 5. The percent of observations that are between 50 and 70 is ______.

The total area of a normal probability distribution is _______.