## Inverse Normal and Continuity Corrections Exercise

1. If Z is the standard normal distribution, find if

a. P(Z < k) = 0.683

b. P(Z < k) = 0.9482

c. P(Z > k) = 0.3834

d. P(Z > k) = 0.9004

 2. The heights of trees follow a normal distribution with mean μ cm and a standard deviation of 1.8 m. It is known that 5% of the trees have a height greater than 8 m. Find the value of the mean, μ.

3. The heights of plants in a nursery are normally distributed with a mean of μ and a variance of 5. 15% of the plants are less than 20 cm tall. Find the probability that a plant chosen at random will be over 25 cm high.

4. The masses of articles produced in a factory are normally distributed with a mean of μ and a standard deviation of σ. 8% of the articles have a mass greater than 90 g and 5% have a mass less than 30 g. Find the values of μ and σ.

5. The weights of corks made by a particular machine are normally distributed.

It is found that 25% weigh over 22 g and 40% weigh under 15 g.

Find the mean and standard deviation of the weights of the corks.

Use a continuity correction for the following three problems:

6. The annual rainfall in Christchurch is measured to the nearest cm and is normally distributed with a mean of 65 cm and a standard deviation of 11 cm. Find the probability that next year the rainfall in Christchurch will be more than 60 cm.

7. The length of movies measured to the nearest minute is normally distributed with a mean of 82 minutes and a standard deviation of 6 minutes. What is the probability that a movie will last between 75 minutes and 95 minutes?

8. The mid-summer average maximum daily temperature in Hokitika as measured over the last 50 years is normally distributed with a mean of 19.7° ( to 1 decimal place)and a standard deviation of 2.1. What is the probability that next year the mid-summer average maximum daily temperature in Hokitika will be more than 20.5°?