Normal Distribution

Question 0

If Sarah received a mark of 60 in her english exam, which had a mean of 54 and a standard deviation of 12. Her english teacher decided to scale her call to have a higher mean of 60 with a standard deviation of 10. What would Sarah’s result now be?

Answer 0

65

Question 1

The length of nails at a factory are normally distributed with a mean length of 6 cm and a standard deviation of 0.05 cm. What percentage of nails has lengths less than 6.05 cm?

Answer 1

84%.

Question 2

A machine set for the production of cylinders of mean diameter 5.00 cm, with a standard deviation 0.020 cm. Assuming a normal distribution, between what values will 95% of the diameters lie?

Answer 2

4.96-5.04 cm

Question 3

A committee of two people is to be chosen at random from a group of five people.

• How many different committees can be formed?
• Stacey is one of the group of five. What is the probability that she is chosen to be on the committee?

Answer 3

• 10

- 2/5

Question 4

In a barrel there are five yellow counters and three green counters. A counter is drawn, its colour noted and a second counter is drawn. The first counter is not replaced in the barrel before the second counter is drawn.

• Calculate the probability that:
• A yellow counter is drawn, followed by a green counter.
• Two counters of a different colour are drawn.
• At least one of the counters are green.

Answer 4

• 15/56
• 13/28
• 9/14

Question 5

A raffle has 1000 tickets that sell for $1 each. There is a first prize of $400, a second prize of $200 and a third prize of $100. Calculate the financial expectation from the purchase of one ticket in the raffle.

Answer 5

Loss of 30 cents per ticket.

Question 6

The digits 5,6,7 and 9 are written on cards and placed face down. Three are then chosen and arranged to form a three-digit number. If this is repeated 150 times, what is the expected number of:

• Odd numbers?
• Numbers greater than 700?

Answer 6

• 112.5

- 75

Question 7

Roofing nails are produced by a machine and the lengths are normally distributed with a mean of 5.00cm and a standard deviation of 0.01 cm. Complete the following:

A) 68% of nails will have a length between …… and ……
B) 95% of nails will have a length between …… and ……
C) 99.7% of nails will have a length between …… and ……

Answer 7

A) 4.99 and 5.01
B) 4.98 and 5.02
C) 4.97 and 5.03

Question 8

A factory makes circular brake discs with a mean diameter of 300mm and a standard deviation of 2mm. The diameters are normally distributed. If diameters more than 3 standard deviations from the mean are rejected, which of these diameters would be rejected?

A) 295mm
B) 307mm
C) 306mm
D) 296mm

Answer 8

B

Question 9

The nicotine content of a brand of cigarette is normally distributed with a mean of 14.5 mg and a standard deviation 1.2 mg. What percentage of the nicotine contents are between 13.3 mg and 15.7 mg?

A) 34%
B) 95%
C) 68%
D) 99.7%

Answer 9

C

Question 10

The expected life of light globes is normally distributed with a mean of 8000 hours.

A) What is the standard deviation if 95% of globes are expected to last between 7700 hours and 8300 hours?
B) Between what two values do 68% of the lifetimes lie?
C) If 12000 light globes are produced, how many are expected to last less than 7850?

Answer 10

A) 150 hours.
B) 7850 and 8150 hours.
C) 1920.