Question

A particular fish population has a mean length of 230 mm and a standard deviation of 50 mm. What is the probability that a random sample of 16 fish from this population has a mean length of at least 240 mm?

Answer 1

Solution :

Given that ,

mean = $\mu$ = 230

standard deviation = $\sigma$ = 50

n = 16

$\mu$ = 230

T

$\sigma$
T
= $\sigma$ / $\sqrt$ n =50 / $\sqrt$16 = 12.5

P(
T
>240 ) = 1 - P(
T
<240 )

= 1 - P[(
T
- $\mu$
T
) / $\sigma$
T
< (240-230) / 12.5]

= 1 - P(z <0.8 )

Using z table

= 1 - 0.7881

= 0.2119

probability=0.2119