# Thread: Normal and Sampling Distribution

1. ## Normal and Sampling Distribution

1. The library checks out an average of 320 books per day, with a standard deviation of 75 books. Consider that the number of books checked out is normally distributed. A sample of 35 days is selected. Find the probability that

a) on one day the number of books checked out is less than 200.
(I got 0.5548??)
b) the sample mean will be between 310 and 340 books.
(got no idea where to start..)

2. Kirks Soft Drinks investigated the performance of their drink filling machines for the "2 litre" bottles of soft drink and found fill amounts which closely resembled a normal distribution with a mean of 1.999litres and a standard deviation of 0.08 litres. The fullest 15% of bottles would be expected to contain more than how many litres of soft drink?

3. Simulated data is frequently used in economic research. A simulated data set may be constructed with the assistance of a random number generator which draws values from between 0 and 1. The values have a mean of 1/2 and a variance of 1/12. Each data set generated consists of 500000 random numbers. If 1000 sets are generated, how many of these sets would we expect to have a mean of no larger than 0.5005.

Your help would be muchly appreciated!!