Question

Suppose that the distribution for total amounts spent by students vacationing for a week in Florida is normally distributed with a mean of 650 and a standard deviation of 120. Suppose you take a SRS of 15 students from this distribution. What is the probability that an SRS of 15 students will spend an average of between 600and700? Round to five decimal places.

Answer 1

Solution:

Given that ,

= 650

= 120

A sample of size n = 15 is taken from this population.

Let be the mean of sample.

The sampling distribution of the is approximately normal with

Mean = = 650

SD =     = 120/​15 =  30.9838667697

Now ,

P(600 < < 700)

= P( < 700) - P( < 600)

= P[( - )/ < (700 - 650)/30.9838667697] - P[( - )/ < (600 - 650)/30.9838667697]

= P[Z < 1.61374] - P[Z < -1.61374]

=  0.94671 - 0.05329 (use z table)

= 0.89342