Question

Heights for group of people normally distributed with mean = 64 inches and standard deviation = 2.4 inches. find the height, h such that about 20% of people in the group are shorter than that height. (round the answer to the nearest tenth.)

Answer 1

62.0 inches The first thing to do is look at a Standard Normal Table to find out how many deviations we need to be from the norm to get 20%. Depending upon the table, you will either be looking for a value of 0.20 or 0.30. The 0.30 is simply 0.50 - 0.20. Use your common sense to determine which value to look for. For instance, in the Standard Normal Table I'm using, a z value of 0 gives me a probability of 0.00000 and a z-value of 4.0 gives me a probability of 0.49997. So I need to look for a probability of 0.30 which is a z-value of approximately 0.84. Now multiply the z-value by the standard deviation. So 0.84 * 2.4 = 2.016 This value of 2.016 means that only 20% of the population are more than 2.016 inches shorter than the mean. So let's calculate that by subtracting that from the mean, giving: 64 - 2.016 = 61.984. Rounding to 1 decimal place gives 62.0 inches.