Exam 5: A Normal World

Assuming that the lengths of the inchworms in Problem 5 are normally distributed, find the 80th percentile of the lengths.

If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, what percentage of light bulbs have a life less than 2500 hours?

Decide which of the described variables likely have a normal or near-normal distribution. a. The amount of change held by a teacher at the end of each day for a year b. The amount of pocket money held by each student at a mid-sized liberal arts college at a Given time c. The number of heads that show when two coins are tosses

The amount of Jen's monthly phone bill is normally distributed with a mean of $50 and a standard deviation of $10. Find the 25th percentile.

If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, what percent of the bulbs will not last as long as 2000 hours? Apply the 68-95-99.7 rule to answer #4 and #5.

There are over 1200 species of inchworms indigenous to North America. Some have been taken to the space station while others provided the idea for neon inchworms from the Jelly Belly Candy Company. One species has a mean length of 0.98 inches and a standard deviation of 0.05 inches. The lengths of 99.7% of these worms will be between ________ and _________ inches.

The diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. In a random sample of 460 pencils, approximately how many would you expect to have a diameter less than 0.293 inches?

Salesmen for the ABC Plastics Company drive an average of 240 miles per day with a standard deviation of 36 miles. If samples of 25 daily mileages are taken, what is the standard deviation of the distribution of sample means?

At one college, GPA's are normally distributed with a mean of 2.9 and a standard deviation of 0.6. Find the 70th percentile.

The lifetimes of projector bulbs of a particular type are normally distributed with a mean of 470 hours and a standard deviation of 15 hours. What percentage of the bulbs has lifetimes that lie within 2 standard deviations of the mean on either side?

A rocket club makes its own rockets. The rockets go to a mean height of 1100 feet with a standard deviation of 60 feet. If the club fires 36 rockets, what is probability that the mean height of the rockets will be greater than 1080 feet?

If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, approximately what percentage of light bulbs has a life of more than 3000 hours?

The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a standard deviation of 1.2 oz. What is the probability that the volume of soda in a randomly selected bottle will be less than 32 oz?

Which of the following two or more statements about the standard normal distribution are always true? a) If b is less than c, then the area to the left of b is less than the area to the left of c. b) If a z-score is negative, then the area to the left of the z-score is negative. c) If a z-score is positive, then the area to the right of the z-score is positive. d) If the area to the right of a z-score is positive, then the z-score is positive.

For a randomly selected inchworm from a normal population with mean 0.98 inches and standard deviation 0.05 inches, find the probability that its length will be between 0.93 inches and 1.02 inches.

If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, use the 68-95-99.7 rule to approximate the percentage of light bulbs having a life between 2000 hours and 3500 hours?

The systolic blood pressures of the patients at a hospital are normally distributed with a mean of 136 mm Hg and a standard deviation of 12 mm Hg. Find the two blood pressures having these properties: the mean is midway between them and 76.98% of all blood pressures are between them.

Select the distribution that appears to be the most normal.

The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.25 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.24 inches?

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 225 and 275.