Question

Nick has collected data to find that the body weights of the forty students in a class has a normal distribution. What is the probability that a randomly selected student has a body weight of greater than 169 pounds if the mean is 142 pounds and the standard deviation is 9 pounds? Use the empirical rule.

Answer 1

mean=142

169-142/9

P(x>169)=1-.997/2

=.15

Explanation:

Answer 2

0.0015 is he probability that a randomly selected student has a body weight of greater than 169 pounds.

Explanation:

We are given the following information in the question:

Mean, μ = 142 pounds

Standard Deviation, σ = 9 pounds

We are given that the distribution of body weights is a bell shaped distribution that is a normal distribution.

Empirical Rule:

• The empirical rule states that for a normal distribution 68% falls within the first standard deviation from the mean, 95% within the first two standard deviations from the mean and 99.7% within three standard deviations of the mean.

P( body weight of greater than 169 pounds)

`169 = 142 + 3(9) = \mu + 3\sigma\\115 = 142-3(9) = \mu - 3\sigma`

According to empirical rule, 99.7% within three standard deviations of the mean.

Thus, we can write:

P( body weight of greater than 169 pounds)

`\displaystyle\frac{1-P(\text{Body weight between 115 and 169})}{2}\\\\= (1-0.997)/(2) = 0.0015`

0.0015 is he probability that a randomly selected student has a body weight of greater than 169 pounds.