## Normal Distribution Exercise

1. Copy and complete the probabilities for the various parts of the following normal distribution graph.

2. The heights of students at a school are normaly distributed with a mean of 172 cm and a standard deviation of 12 cm.

a. What percentage of students have heights between 160 cm and 184 cm?

b. What percentage of students have heights of more than 196 cm?

c. What percentage of students have heights less than 184 cm?

d. What percentage of students have heights between 136 cm and 196 cm?

3. Use the standard normal tables to find the following probabilities.

a. P( 0 < Z < 1.6)

b. P( -1.24 < Z < 0)

c. P( -0.983 < Z < 1.456)

d. P( Z < 1.93)

4. A normal distribution has a mean μ = 12 and a standard deviation σ = 2. Use the formula  to help find the probabilities that:

a. P( 10 < x < 13.5)

b. P( 12.5 < x < 14)

c. P( x > 11)

d. P( x < 9.6)

 5. Two brands of light bulbs, brand Everlast and brand Allglo have the same average life of 75 hours with standard deviations of 2.25 hours and 2.75 hours respectively. For each brand, what is the probability that a bulb chosen at random will have a life of more than 70 hours?

6. A normal distribution of a continuous variable has a mean of 21.2 and a standard deviation of 3.1.

a. Find the probability that a value selected at random will between 15 and 30.

b. Above what value do 80% of the values lie?

c. Below what value do 90% of the values lie?

7. The average yearly rainfall of a town, recorded since records began, is normally distributed with a mean of 95 cm and a standard deviation of 28 cm.

a. What is the probability that a year selected at random will have a rainfall between 50 and 100 cm?

b. In a period of 100 years, how many years could it be expected that the town would have less than 47.5 cm of rain?

 8. The weights of kiwifruit from an export order to the US is normally distributed with a mean of 520 g and a standard deviation of 52 g. a. What percentage of all kiwifruit would be expected to weigh between 450 g and 600 g? b. In a load of 5000 kiwifruit, how many kiwifruit would be below 400 kg? c. Below what weight would 95% of the kiwifruit lie?