Question

The population of bluegills (type of fish) has a mean length of 152.09mm and a standard deviation of 19.62mm. What is the probability that a random sample of 25 fish has a mean length of 140mm or shorter

Answer 1

Answer:

0.001035

Step-by-step explanation:

Mean (m) = 152.09 mm

Standard deviation (σ) = 19.62 mm

Sample size (n) = 25

Length being 140mm or shorter (x) : x ≤ 140

Using the Zscore relation :

Zscore = (x - m) / (σ/√n)

Zscore = (140 - 152.09) / (19.62/√25)

Zscore = (140 - 152.09) / (19.62/5)

Zscore = −3.081039

P(Z ≤ −3.08) = 0.001035