Question

The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 97 inches, and a standard deviation of 16 inches. What is the probability that the mean annual snowfall during 64 randomly picked years will exceed 998 inches? Round your answer to four decimal places O A 0.4192 OB 0.0026 OC. 0.5808 OD. 0.0808

Answer 1

Solution :

Given that,

mean = $\mu$ = 97

standard deviation = $\sigma$ = 16

n = 64

$\mu$
_T
= 97

$\sigma$
_T
= $\sigma$ / $\sqrt$ n = 16 / $\sqrt$ 64 = 2

P(
T
> 99.8 ) = 1 - P(
T
< 99.8 )

= 1 - P[(
T
- $\mu$
_T
) / $\sigma$
_T
< ( 99.8 -97) / 2]

= 1 - P(z < 1.4)

Using z table,    

= 1 - 0.9192

= 0.0808

Probability = 0.0808

Correct option : D. 0.0808