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Advanced Algebra Statistics Day 3 Name_____________ WS Normal Distribution
- The diameters of metal fittings made by a machine are normally distributed. The mean diameter is 7.5 cm, and the standard deviation is .5 cm.
a. What percentage of the fittings have diameters between 7cm and 8cm?
b. What percentage of the fittings have diameters between 7.5cm and 8cm?
c. What percentage of the fittings have diameters greater than 6.5cm?
d. Of 100 fittings, how many will have a diameter between 6cm and 8.5cm?
- The lifetimes of 10,000 light bulbs are normally distributed. The mean lifetime is 300 days, and the standard deviation is 40 days.
a. How many light bulbs will last between 260 and 340 days?
b. How many light bulbs will last between 220 and 380 days?
c. How many light bulbs will last less than 300 days?
d. How many light bulbs will last more than 300 days?
e. How many light bulbs will last more than 380 days?
f. How many light bulbs will last less than 180 days?
- Jalisa and Wes were conducting an experiment in statistics. They asked each student in their mathematics classes to toss a fair coin 100 times and record the number of heads they obtained. They found that the number of heads was almost distributed normally. The mean number of heads was 50 and the standard deviation was 5.
a. What percentage of the students who tossed the coins obtained less than 50 heads?
b. What percentage of the students who tossed the coins obtained between 35 and 45 heads?
c. What percentage of the students who tossed the coins obtained between 40 and 60 heads?
- The weight of boxes of cereal filled by a machine are normally distributed. The mean weight is 510 gms with a standard deviation of 4 gms.
a. Of 1000 boxes, how many weigh at least 510 gms?
b. Of 1000 boxes, how many weigh between 502 and 514 gms?
c. A machine at the end of the production line checks the weight of the boxes before they are shipped to the stores. If a box weighs more than 522 gms, it is sent back to the beginning of the line to be emptied and reused. Of 1000 boxes, how many will be sent back for this reason?
d. The machine that checks the weight of the boxes sends back boxes that weigh less than 502 gms. Of 1000 boxes, how many will be sent back for this reason?
