The height of a certain population of corn plants follow a normal distribution with mean 145 cm and standard deviation 22 cm.  a) What percentage of the plants are between 135 and 155 cm tall? b) 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 he sample mean height between 135 and 155 cm? c) If Ŷ represents the mean height of a random sample of 36 plants from the population, what is P{ 135<=Ŷ <=155}?

Human Anatomy & Physiology (11th Edition)
11th Edition
ISBN:9780134580999
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Chapter1: The Human Body: An Orientation
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The height of a certain population of corn plants follow a normal distribution with mean 145 cm and standard deviation 22 cm. 
a) What percentage of the plants are between 135 and 155 cm tall?
b) 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 he sample mean height between 135 and 155 cm?
c) If Ŷ represents the mean height of a random sample of 36 plants from the population, what is P{ 135<=Ŷ <=155}?

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