Use the normal distribution of fish lengths for which the mean is 8 inches and t

Question

Use the normal distribution of fish lengths for which the mean is 8 inches and the standard deviation is 4 inches. Assume the variable x is normally distributed. (a) What percent of the fish are longer than 13 inches? (b) If 400 fish are randomly selected, about how many would you expect to be shorter than 7 inches? (a) Approximately % of fish are longer than 13 inches. (Round to two decimal places as needed.) (b) You would expect approximately fish to be shorter than 7 inches. (Round to the nearest fish.)

Explanation / Answer

a)proportion of fish longer then 13 inches =P(X>13|)=1-P(X<13)=1-P(Z<(13-8)/4)=1-P(Z<1.25)

=1-0.8944=0.1056

therefore 10.56% of fish are longer then 13 inches,

b)for n=400

std error=std deviation/(n)1/2 =4/(400)1/2 =0.2

proportion of fish shorter then 7 inches =P(X<7)=P(Z<(7-8)/0.2)=P(Z<-5)=0.0000

therefore expected =400*0.0000=0.00 fish to be shorter then 7 inches,

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