Exam 7: Continuous Probability Distributions

The mean amount spent by a family of four on food is $500 per month 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?

In a standard normal distribution, µ = ______ and σ = _____.

About ______% of the area under the normal curve is within plus two and minus two standard deviations of the mean.

For a normal distribution, what is the likelihood (expressed as a percentage) that a random variable is within plus and minus two standard deviations of the mean?

The shape of the uniform distribution is ___________.

The proportion of the area under a normal curve that is to the right of z = -1.71 is _______.

The proportion of the area under a normal curve that is to the left of z = 1.40 is _______.

When referring to the normal probability distribution, there is not just one; there is a "family" of normal probability distributions.

The seasonal output of a new experimental strain of pepper plants was carefully weighed. The mean weight per plant is 15.0 pounds, and the standard deviation of the normally distributed weights is 1.75 pounds. Of the 200 plants in the experiment, how many produced peppers weighing between 13 and 16 pounds?

For the standard normal distribution, the z-score that corresponds with the first quartile is ________.

The upper and lower limits of a uniform probability distribution are __________.

Two business major students, in two different sections of an economics class, were comparing test scores. The following shows the sections' mean and standard deviation. The student in section 1 scored 84, while the student in section 2 scored 75. The student from section _____ scored better compared than the rest of the section.

Customers of the Key Refining Company charge an average of $70 per month. The distribution of amounts charged is approximately normal, with a standard deviation of $10. What is the probability of selecting a credit card customer at random and finding the customer charged between $70 and $83?

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 less than 135 minutes?

The mean score of a college entrance test is 500; the standard deviation is 75. The scores are normally distributed. What percent of the students scored below 320?

For the normal distribution, the mean plus and minus two standard deviations will include about what percent of the observations?

The annual commissions per salesperson employed by a retailer of mobile communication devices averaged $40,000, with a standard deviation of $5,000. What percent of the salespersons earn between $32,000 and $42,000?

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 23 ounces is ____.

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

The standard normal probability distribution is unique because it has _________.