1. If Z is the standard normal distribution, find k 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
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°?
