Question

The heights of mature Iowan corn stalks are normally distributed with mean height of 95 inches with standard deviation of 10 inches. What is the probability that a random sample of 100 mature Iowan corn stalks will have mean height more than 96 inches?

Answer 1

Let denote heights (in inches) of a random sample of size n = 100 of mature Iowan corn stalks. Now, we are given that heights of mature Iowan corn stalks are normally distributed with mean height of 95 inches and standard deviation of 10 inches.

Thus, we get:

Let be the sample mean height of these 100 Iowan corn stalks, i.e.,

Thus, the distribution of is given by:

Now, the probability that a random sample of 100 mature Iowan corn stalks will have mean height more than 96 inches is given by:

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