Question

2. I have a distribution of data that is skewed left with a mean of 50 and a standard deviation of 15. I take 5000 samples each of size 11 from this data set. Then the sampling distribution of sample means will have:

a) Mean = _______ b) Standard deviation = _____________ c) What shape distribution= _______

3. The mean length of time it takes for a broken arm to heal is normally distributed with a mean of 44 days and a standard deviation of 7 days.

a) Find the probability one person with a broken arm will heal in over 38 days?

b) Find the probability from a sample of 45 people with broken arms that the average time for the sample of 45 to heal is over 38 days?

c) Why is your answer for part b) greater than the answer for part a)?

d) Give an example of an interval that could have been used in parts a) and b) so that the answer for b) is less than the answer for a)?

Answer 1

2. We have given that  a distribution of data that is skewed left .

5000 samples each of size 11 from this data set

So n=11

The sampling distribution of the mean approaches a normal distribution as sample size (n) increases.

Then the sampling distribution of sample means will have:

a) Mean = = 50

b) Standard deviation =  

= 4.52

c) Shape of the distribution would be Normal or bell shape.