Normal Probability (117 problems)

The serum cholesterol levels of the male patients at a hospital are normally distributed with a mean of 178.7 (mg/100ml) and a standard deviation of 40.6. Find the two serum cholesterol levels having these properties: the mean is midway between them and 90% of all serum cholesterol levels are between them.

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?

Assume that the salaries of elementary school teachers in the U.S. are:

Normally distributed

Standard deviation: $5,000

What is the cutoff salary for teachers in the bottom 10%?

The amount of time it takes a student to walk from her home to class has a:

Skewed right distribution

Mean: 16 mins.

Standard deviation: of 1.6 mins. If data were collected from 30 randomly selected walks, describe the sampling distribution of the sample mean time.

If the lathe can be adjusted to have the mean of the lengths to any desired value, what should it be adjusted to? Why?

Thirty randomly selected students took the statistics final. If the sample mean was 81.4 and the standard deviation was 12.0, construct a 99 percent confidence interval for the mean score of all students.

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. For a randomly selected bottle of soda, find the percentage of quart bottles where the volume of soda will be greater than 32 oz?

For a random variable that is normally distributed, with µ = 200 and ơ = 20, determine the probability that a simple random sample of 4 items will have a mean that is

a) Greater than 210.
b) Between 190 and 230.
c) Less than 225.

Suppose that the distribution of human pregnancies is approximately normal with mean u = 266 days and standard deviation sigma = 16 days
a. what percent of human pregnancies last between 250 and 270 days

b. what percent last less then 280 days

c. what percent last at least 260 days

d. the longest 10% are longer then how many days

e. the shortest 25% are shorter then what number of days

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 150 and 230.

The amount of corn chips dispensed into a 20-ounce bag by the dispensing machine with a:

Normal distribution

Mean: 20.5 ozs.

Standard deviation: 0.2 oz.

What proportion of the 20 oz bags contain more than the advertised 20 ozs.?

The amount of rainfall in January in a certain city is normally distributed with a mean of 3.7 inches and a standard deviation of 0.5 inches. The value of Q₂ is 4.0.

Designing Helmets Engineers must consider the breadths of male heads when determining motorcycle helmets. Men have heads breadths that are normally distributed with a mean of 6.0 in. and a standard deviation of 1.0 in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 2.5% or largest 2.5%. Find the minimum and maximum head breadths that will fit men.

The average cost of a home in Red Wing, Indiana, is $92,000 and the standard deviation is $8,400. What is the probability that a house in Red Wing will cost at least $98,000? List all pertinent information and draw a graph.

The participants in a television quiz show are picked from a large pool of applicants with approximately equal numbers of men and women. Among the last participants there have been only 2 women. Using the binomial printout below, what is the probability of not getting 2 or fewer women when 10 people are picked?

The length of time to complete a door assembly on a automobile factory assembly line is normally distributed with mean = 6.7 minutes and standard deviation = 2.2 minutes. For a door selected at random, what is the probability the assembly line will be

a) 5 minutes or less

b) 10 minutes or less

c) between 5 and 10 minutes

d) more then 10 minutes

For the 400 seniors at a high school, the mean score on a standard college entrance exam is 480 and the standard deviation is 100. If a sample of 36 of these students is randomly selected without replacement, find the probability that mean for this sample group is above 500.

The amount of rainfall in January in a certain city is normally distributed with a mean of 3.4 inches and a standard deviation of 0.5 inches. Use the concepts learned in Chapter 5 to find the value of Q₁ .

Suppose that the number of ounces of soda put into a Pepsi can is normally distributed with μ=12.05 ounces and σ =0.03 ounces.

a) Legally a can must contain at least 12 ounces of soda. What fraction of cans will contain at least 12 ounces of soda?

b) Pepsi controls the mean weight in a can by setting a timer. For what mean should the timer be set so that only 1 in 1000 cans will be underweight?

c) Every day Pepsi produces 10,000 cans. The government inspects 10 randomly chosen cans each day. If at least two are underweight, Pepsi is fined $10,000. Given that μ=12.05 ounces and σ =0.03 ounces, what is the probability that Pepsi will be fined on a given day?