Question

The mean age of salesladies in an ABC department store is 32 , with a standard deviation of 8 . Between which two age limits must 75% of the data set lie?

Answer 1

To find the age limits within which 75% of the data set lies, we need to calculate the z-scores for the upper and lower quartiles and use them to find the age limits. The lower age limit is 26.604 years and the upper age limit is 37.396 years.

Step-by-step explanation:

To find the age limits within which 75% of the data set lies, we need to find the z-scores corresponding to the upper and lower quartiles. Since the distribution is normal, we can use the standard normal distribution table to find the z-scores. The z-score corresponding to the lower quartile (25th percentile) is -0.674, and the z-score corresponding to the upper quartile (75th percentile) is 0.674.

Using the z-score formula, we can calculate the age limits:

Lower limit = mean - (z-score * standard deviation) = 32 - (0.674 * 8) = 26.604

Upper limit = mean + (z-score * standard deviation) = 32 + (0.674 * 8) = 37.396

Therefore, 75% of the data set lies between the ages of 26.604 and 37.396 years.