Z-score test

The fish weights in a certain lake are normally distributed with a mean of 11 lb and a standard deviation of 6. If four fish are randomly selected, what is the probability that the mean weight will be between 8.6 and 14.6 lb? Your answer should be a decimal rounded to the fourth decimal place.

Correct answer:

p =  0.673

Step-by-step explanation:

μ=11 lb σ=6 lb  n=4 s=σ/n=6/4=3 lb  z =  sX  μ x1=8.6 lb x2=14.6 lb  z1=sx1μ=38.611=54=0.8 z2=sx2μ=314.611=56=151=1.2  p1 = N(z<z1) p1=0.2119 p2 = N(z<z2) p2=0.8849  p=p2p1=0.88490.2119=1000673=0.673

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