The mean weight of a group of boys is 150 lb, with a standard deviation of 20 lb. If the weights are normally distributed, find the probability that one of the boys picked at random from the group weighs more than 178 lb. Use a table of the standard normal distribution to solve the problem. Round your answer to four decimal places.
A)0.9192
B)0.4192
C)0.4278
D)0.2318
E)0.0808

Question

The mean weight of a group of boys is 150 lb, with a standard deviation of 20 lb. If the weights are normally distributed, find the probability that one of the boys picked at random from the group weighs more than 178 lb. Use a table of the standard normal distribution to solve the problem. Round your answer to four decimal places. ​
A)​0.9192
B)​0.4192
C)​0.4278
D)​0.2318
E)​0.0808

Quizplus · Accepted Answer

To find the probability that a boy weighs more than 178 lb, we first convert the weight to a z-score using the formula $z = \frac{X - \mu}{\sigma}$, where $X$ is the weight, $\mu$ is the mean, and $\sigma$ is the standard deviation. Plugging in the values, we get $z = \frac{178 - 150}{20} = 1.4$. Looking up 1.4 in a standard normal distribution table gives the area to the left of 1.4, which is approximately 0.9192. To find the probability of being more than 178 lb, we subtract this from 1, giving $1 - 0.9192 = 0.0808$.

The Mean Weight of a Group of Boys Is 150