A recent botany experiment showed a variety of results for the height of certain plants. The results followed a normal distribution with a mean of 8.4 feet and a standard deviation of 2.2 feet. Find the probability that a randomly selected plant with have a height less than 6.0 feet.

A.

0.9861

B.

0.7257

C.

0.9621

D.

0.1379

Answer: About 13.79% of the plants will have a height of less than 6.0 feet.

To answer this question, we first need to know how many standard deviations it is below the mean. That is called the z-score.

To find the z-score, we determine the difference of the expected value and the mean. Then, we divide that by the standard deviation.

(6 - 8.4) / 2.2 = - 1.09

A height of 6 is - 1.09 standard deviations below the mean. Looking up the probability for a z-score of - 1.09 gives us a value of 13.79%.