Download AP Statistics Name The Standard Normal Curve Show all work for

AP Statistics
The Standard Normal Curve
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1. Researchers observed a set of students who lived at the Simpson Dormitory on the campus of Miami
University. The length of time it took students to walk from the dorm to their Statistics class in
Brink Hall was timed for each student. The distribution of times was normally distributed with a
mean of 18 minutes and a standard deviation of 5 minutes. Of the 250 students in Simpson Dorm, how
many take more than 25 minutes to get to class?
2. The amount of cereal in a box of Tamara's Treats is supposed to be 27 oz. However, since machines pack
the boxes, the weight varies slightly from box to box. The distribution of the weight in each box is
approximately normally distributed with a mean weight of 27 oz. and a standard deviation of .25 oz. The
manufacturers reject a box if it weights less than 26.3 oz. or more than 27.4 oz. Out of 2000 boxes
manufactured today, how many should one expect to be rejected?
3. At the Media Center at Chen's High School for the Highly Literate, the average student usually checks
out some books every time he or she goes to the Media Center. The distribution of the number of books
checked out is approximately normal with a mean of 4 and a standard deviation of 1.5. If 500 students
visit the Media Center on Monday, how many can be expected to check out 6 or more books? How many
will check out zero books?
4. At the Fogwell Company, computer parts are made. The distribution of the lengths of the frazzer is
approximately normal with a mean length of .41 cm and a standard deviation of .045 cm. The acceptable
range for a part is to be between .4 and .42 cm. Of the 10,000 frazzers made this month, how many will
probably need to be rejected?
5. The Lemr Light Company makes light bulbs. When doing a quality control check of light bulbs, the head
statistician, Daniel, noted that the mean life of a 60 W bulb was 1200 hours. The distribution of the
lifetimes was about normal with a standard deviation of 42 hours. A bulb is considered defective if it
lasts less than 1100 hours. Of the 5000 bulbs sold in May, how many should be expected to be defective?
6. The mean weight of men at Imabigguy College is 190 lbs. with a standard deviation of 25 pounds. How
many of the 700 men are eligible for the dorm’s “Skinny Dude Lunch”, available for those weighing 140 lbs.
or less? How many are eligible for the “Large and in Charge Meal” for those weighing more than 230 lbs?
7. A traffic study on I-71 North outside of Middleburg Hts. shows that the average speed of vehicles on the
weekend is normally distributed with a mean speed of 64 mph and a standard deviation of 6.2 mph. What
proportion of the drivers is above the speed of 60 mph? 75 mph? What proportion are “hyper-speeders”,
that is, going more than 80 mph? What proportion is below the minimum speed of 45 mph?
8. In the country of Choekovia, the distribution of female heights has a mean height of 63 inches with a
standard deviation of 2.35 in. What proportion of the females are less than five feet tall? What
proportion are between 60 in. and 68 in. in height?
9. The average age of media reporters worldwide is 35 years with a standard deviation of 6 years. If
Masterson Media employs 50 media reporters, then what is the probability that their mean age lies
between 34 and 37 years? Assume that the variable is normally distributed.