Question

A distribution of values is normal with a mean of 160 and a standard deviation of 5.

Find the interval containing the middle-most 32% of scores:

Enter your answer accurate to 1 decimal place using interval notation. Example: (2.1,5.6)


Hint: To work this out, 1) sketch the distribution, 2) shade the middle 32% of the data, 3) label unkown data values on the horizontal axis just below the upper and lower ends of the shaded region, 4) calculate the percentage (area) to the left of the lowermost unknown data value, 5) calculate the TOTAL percentage (area) to the LEFT of the uppermost unknown data value, 6) use invnorm to calculate the lowermost data value, 7) use invnorm to calculate the uppermost data value. The data values you get from steps 6 and 7 are used to answer the question.

Answer 1

Solution:

Now to find the lower value, we need to find the z-value corresponding to area = 0.34. Using the standard normal table, we have:

Now using the z-score formula, we have:

Now to find the upper value, we need to find the z-value corresponding to area = 0.66. Using the standard normal table, we have:

Now using the z-score formula, we have:

Therefore, the interval containing the middle-most 32% of scores is 157.9 and 162.1