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aleksklad [387]
3 years ago
5

Use the normal distribution of fish lengths for which the mean is 11 inches and the standard deviation is 2 inches. assume the v

ariable x is normally distributed. left parenthesis a right parenthesis what percent of the fish are longer than 12 ?inches
Mathematics
1 answer:
Kaylis [27]3 years ago
3 0

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.

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