The Curve
Label the normal distribution curve given a mean of 143 and a standard deviation of 8.
(119, 127, 135, 143, 151, 159, 167)
The weight of chocolate bars from a particular chocolate factory has a mean of 8 ounces with a standard deviation of 0.1 ounces. What is the z-score corresponding to a weight of 8.17 ounces?
z = 1.7
What is the z score, given the p value of .99010
z = 2.33
A large group of students took a test in Physics and the final grades have a mean of 70 and a standard deviation of 10. If we can approximate the distribution of these grades by a normal distribution, what percent of the students scored above an 85.
6.681%
The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days. About what percent of the products last 6 days or less?
2.5%
(60.1, 64.4, 68.7, 73, 77.3, 81.6, 85.9)
Books in the library are found to have an average length of 350 pages with a standard deviation of 100 pages. What is the z-score corresponding to a book of length 80 pages?
z = -2.7
What is the z score, given the p value .01101
z = -2.29
Find the probability that the shopper will be in the store more than 39 minutes. (Recall that μ = 45 minutes and σ = 12 minutes.)
.30854
In an Oreo factory, the mean mass of a cookie is given as 40 g. For quality control, the standard deviation is 2 g. What percent of Oreas have a mean less than 44g?
97.5%
Ms. Pickett's AP chem class took a practice AP Chem exam. The scores followed a normal distribution with an average of 81 and a deviation of 5.2. Label a curve given the information.
(65.4, 70.6, 75.8, 81, 86.2, 91.4, 96.6)
A particular leg bone for dinosaur fossils has a mean length of 60 inches with a standard deviation of 3 inches. What is the z-score that corresponds to a length of 62 inches?
z = 0.67
What is the z score, given the p value .59871
z = 0.25
A survey indicates that people use their computers an average of 2.4 years before upgrading to a new machine. The standard deviation is 0.5 year. A computer owner is selected at random. Find the probability that he or she will use it for fewer than 2 years before upgrading. Assume that the variable x is normally distributed.
.21186
The mean life of a tire is 30,000 km. The standard deviation is 2000 km. What percent of the tires will have a life longer than 32,000 km?
16%
A professor at Boston College curved his students grades on a recent test. The average grade was a 73 with a deviation of 2.7. Label a normal distribution curve.
(64.9, 67.6, 70.3, 73, 75.7, 78.4, 81.1)
In the 24-25 season, the Duke Blue Devils have an average of 79.7 points per game with a deviation of 7.9. What is the z score for their game against University of Kentucky where they scored 72 points.
z = -0.97
What is the z score, given the p value .00009
z = -3.74 or -3.75
A survey indicates that for each trip to the supermarket, a shopper spends an average of 45 minutes with a standard deviation of 12 minutes in the store. The length of time spent in the store is normally distributed and is represented by the variable x. A shopper enters the store. Find the percent of shoppers that will be in the store for between 24 and 54 minutes.
73.331%
The monthly income of 5,000 workers at the Microsoft plant are distributed normally. Suppose the mean monthly income is $1250 and the standard deviation is $250. What percentage of the workers earn between $750 and $1500 per month?
81.5%
In the 24-25 season, the Duke Blue Devils are averaging 79.7 points per game with a deviation of 7.9 points. Label a normal curve.
(56, 63.9, 71.8, 79.7, 87.6, 95.5, 103.4)
The temperature is recorded at 60 airports in a region. The average temperature is 67 degrees Fahrenheit with a standard deviation of 5 degrees. What is the z-score for a temperature of 68 degrees?
z = 0.20
What is the z score, given the p value .99984
z = 3.60
Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. Nate takes the test and scores 585. What is Nate's score as a percent?
80.234%
A grading scale is set up for 1000 students’ test scores. It is assumed that the scores are normally distributed with a mean score of 75 and a standard deviation of 15. If 60 is the lowest passing score, how many students are expected to pass the test?
840 students are expected to pass.