Answer: 0.688
Step-by-step explanation:
Given: Mean : [tex]\mu = 481 \text{ millimeters}[/tex]
Standard deviation : [tex]\sigma=871\text{ millimeters}[/tex]
Sample size : [tex]n=1600[/tex]
We assume these lengths are normally distributed.
Then the formula to calculate the z score is given by :-
[tex]z=\dfrac{X-\mu}{\sigma}[/tex]
For X=501
[tex]z=\dfrac{501-481 }{41}=0.487804878049\approx0.49[/tex]
The p-value of z =[tex]P(z<0.49)=0.6879331\approx0.688[/tex]
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
