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

and standard deviation

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)​

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  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)

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