Question

The mean length of six-year-old rainbow trout in the Arolik River in Alaska is 481 millimeters with a standard deviation of 41 millimeters. Assume these lengths are normally distributed. What proportion of six-year-old rainbow trout are less than 501 millimeters long?

Answer 1

Answer: 0.688

Step-by-step explanation:

Given: Mean : $\mu = 481 \text{ millimeters}$

Standard deviation : $\sigma=871\text{ millimeters}$

Sample size : $n=1600$

We assume these lengths are normally distributed.

Then the  formula to calculate the z score is given by :-

$z=\dfrac{X-\mu}{\sigma}$

For X=501

$z=\dfrac{501-481 }{41}=0.487804878049\approx0.49$

The p-value of z =$P(z$

Now, the probability of the newborns weighed between 1492 grams and 4976 grams is given by :-

Hence, The proportion of six-year-old rainbow trout are less than 501 millimeters long = 0.688