Sample size from specified margin of error at 95% CI

I am trying to work through a statistics tute and need some help figuring out this question:

A sample of 50 people was selected and found to have spent an average of 31 hours per week on household chores. Assume that the population standard deviation is 4 hours. Then a 95% confidence interval for the mean time spent completing these tasks is calculated to be 29.891 to 32.109 hours. What is the additional sample size required in order to have a margin of error equal to 1 hour with 95% confidence?

I would appreciate if you can show the working as this question has me very confused D:

Jane -

In order to have a margin of error equal to 1 hour with 95% confidence, you want the following equation to be true:

1 = 1.96(4/sqrtN)

Here is the explanation: (4/sqrtN) is the sample standard deviation. 1.96 is the z-value associated with the 95% confidence interval.

Now, solve for N:

1 = 1.96(4/sqrtN)

sqrtN = 1.96(4) = 7.84, next square both sides

N = 61.5

So, add 12 to 50 to make your sample size equal 62 and this will produce a margin of error equal to 1.

Hope that helped