Question

Solve the problem. The weights of the fish in a certain lake are normally distributed with a mean of 18 lb and a standard deviation of 9. If 9 fish are randomly selected, what is the probability that the mean weight will be between 15.6 and 21.6 lb?

Answer 1

ANSWER:

Given that,

Solve the problem. The weights of the fish in a certain lake are normally distributed with a mean of 18 lb and a standard deviation of 9. If 9 fish are randomly selected, what is the probability that the mean weight will be between 15.6 and 21.6 lb?

Mean = = 18 lb

Standard deviation = = 9

Sample size = n = 9

The probability that the mean weight will be between 15.6 and 21.6 lb.

P(15.6 < x < 21.6) = P((15.6-18) / (9/sqrt(9)) < (x-) / (/sqrt(n)) < (21.6-18)/(9/sqrt(9)))

P(15.6 < x < 21.6) = P((-2.4 / 3) < z < (3.6/3))

P(15.6 < x < 21.6) = P(-0.8 < z < 1.2)

P(15.6 < x < 21.6) = P(z < 1.2)-P(z < -0.8)

P(15.6 < x < 21.6) = 0.88493 -0.21186 (From z score table as given below)

P(15.6 < x < 21.6) = 0.67307

(Rounded to four decimal places)

P(15.6 < x < 21.6) = 0.6731

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