Question

The heights of a certain population of corn plants follow a normal distribution with mean 145cm

and standard deviation 22 cm.

1 What percentage of the plants are between 135 and 155 cm tall?

2 Suppose we were to choose at random from the population a large number of samples of 16 plants

each. In what percentage of the samples would the sample mean height be between 135 and 155cm?

3 If X represents the mean height of a random sample of 16 plants from the population, what is

P(135 ≤ X ≤ 155)

4 If X represents the mean height of a random sample of 36 plants from the population, what is

P(135 ≤ X ≤ 155)​

Answer 1

Answer:

The heights of a certain population of corn plants follow a normal distribution with mean 145cm

and standard deviation 22 cm.

1 percentage of the plants are between 135 and 155 cm tall?

2 Suppose we were to choose at random from the population a large number of samples of 16 plants

each. In percentage of the samples would the sample mean height be between 135 and 155cm

3 If X represents the mean height of a random sample of 16 plants from the population, is

P(135 ≤ X ≤ 155)

4 If X represents the mean height of a random sample of 36 plants from the population,

P(135 ≤ X ≤ 155)