Question

In a certain winter vacation city, snowfalls in January are Normally distributed with mean = 175.8 inches and standard deviation = 25.8 inches. A researcher randomly selects 36 snowfalls. What is the probability that the mean of the sample is less than 170 inches? What is the probability that the mean of the sample is greater than 180 inches?

Answer 1

Solution :

Given that,

mean = = 175.8

standard deviation = =25.8

n = 36

= 175.8

₌ / n = 25.836 = 4.3

( < 170 )

P ( - /) < (170- 175.8 /4.3)

P( z < - 5.8 /4.3 )

P ( z < - 1.35 )   

Using z table

= 0.0885

Probability = 0.0885

ii P ( > 180 )

= 1 - P ( < 180)

= 1 - P ( - /) < (180 - 175.8 /4.3 )

= 1 - P( z < 5.8 / 4.3 )

= 1 - P ( z < 1.35 )   

Using z table

= 1 - 0.9115

= 0.0885

Probability = 0.0885