Question

A fish story: The mean length of one-year-old spotted flounder, in millimeters, is 133 with standard deviation of 20, and the mean length of two-year-old spotted flounder is 156 with a standard deviation of 24. The distribution of flounder lengths is approximately bell-shaped.

(a) Anna caught a one-year-old flounder that was 145 millimeters in length. What is the z-score for this length? Round the answers to at least two decimal places.

(b) Luis caught a two-year-old flounder that was 195 millimeters in length. What is the z-score for this length? Round the answers to at least two decimal places.

(c) Joe caught a one-year-old flounder whose length had a z-score of 1.3. How long was this fish? Round the answer to at least one decimal place.

(d) Terry caught a two-year-old flounder whose length had a z-score of −0.6. How long was this fish? Round the answer to at least one decimal place.

Answer 1

Solution :

Given that ,

mean = = 133 ( one year)

standard deviation = = 20

mean = = 156 ( two year)

standard deviation = = 24

a) x = 145

Using z-score formula,

z = x - /   

z = 145 - 133 / 20

z = 0.60

b) x = 195

Using z-score formula,

z = x - /   

z = 195 - 156 / 24

z = 1.63

c) Using z-score formula,

z = 1.3

x = z * +

x = 1.3 * 20 + 133

x = 159

d) Using z-score formula,

z = -0.6

x = z * +

x = -0.6 * 24 + 156

x = 141.6