It is known that the mean number of days per year that business travellers are on the road for business is 115. The standard deviation is 60 days per year. Assume that these results apply to the population of business travellers and the sample of 50 business travellers will be selected from a normally distributed population.

What is the probability that the average number of days will be within 5 days of the population mean?

Question

It is known that the mean number of days per year that business travellers are on the road for business is 115. The standard deviation is 60 days per year. Assume that these results apply to the population of business travellers and the sample of 50 business travellers will be selected from a normally distributed population.


What is the probability that the average number of days will be within 5 days of the population mean?

anonymous · Answer

The standard error of the mean is the standard deviation of the
sample divided by the square root of the number in the sample making up the mean. s.e. = 60/sqrt(50)= 8.5. 

The means are distributed more nearly normally than the population from which they come, so the distributions of means can be assumed nearly normal [Student's t test for large samples, etc.]

find the area of the normal distribution that comes within +-  (5/8.5) standard deviations of the mean to get your probability. 

If it had been +- 1 one standard deviation, this would be.84-.16=.68.

anonymous · Answer

@douglaswinslowcooper so the answer is 0.58? am i correct? or is there more to it :-/