Question

The monthly electrical utility bills of all customers for the Far East Power and Light Company are known to be distributed as a normal distribution with mean equal to $187.00 a month and standard deviation of $36.00. If a statistical sample of n = 100 customers is selected at random, what is the probability that the mean bill for those sampled will exceed $175.00?

Group of answer choices

3.33

-0.33

Approximately 0.63

About 1.00

Answer 1

Solution :

Given that ,

mean = = 187

standard deviation = =36

n = 100

= 187

= / n = 36 / 100 = 3.6

P( >175 ) = 1 - P( < 175)

= 1 - P[( - ) / < (175-187) / 3.6]

= 1 - P(z < -3.33)

Using z table

= 1 - 0.0004

=0.9996

=1.00