Question

Use the normal distribution of fish lengths for which the mean is 11 inches and the standard deviation is 2 inches. assume the variable x is normally distributed. left parenthesis a right parenthesis what percent of the fish are longer than 12 ?inches

Answer 1

To solve this problem, we make use of the z statistic. What we have to do here is to find for the z score using the given data and from the standard probability tables for z, we locate the proportion of the fish longer than 12 inches.

The formula for calculating the z score is:

z = (x – μ) / σ

where,

x = the sample value = 12 inches

μ = the sample mean = 11 inches

σ = 2 inches

so,

z = (12 – 11) / 2

z = 1 / 2

z = 0.5

Since we are looking for the values greater than 12, so this is a right tailed test. Using the tables, the value of p at this value of z is:

p (z = 0.5) = 0.3085

Therefore there is a 30.85% probability that the fish is longer than 12 inches.