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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?

Respuesta :

JeanaShupp

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

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