Use a normal distribution with μ = 64.5 and σ = 2.0 to approximate the percentage of these students having heights within any specified range. In each part, (i) obtain the exact percentage from the table, (ii) use the normal distribution to approximate the percentage, and (iii) compare your answers.
a. The percentage of female students with heights between 62 and 63 inches.
(i) The actual percentage of female students with heights between 62 and 63 inches is ______ %.
(Type an integer or a decimal.)
(ii) The normal distribution approximates the percentage of female students with heights between 62 and 63 inches to be ______ %.
(Round to two decimal places as needed.)
(iii) The approximate percentage is (1) ______ the actual percentage.
b. The percentage of female students with heights between 64 and 68 inches.
(i) The actual percentage of female students with heights between 64 and 68 inches is ______ %.
(Type an integer or a decimal.)
(ii) The normal distribution approximates the percentage of female students with heights between 64 and 68 inches to be ______ %.
(Round to two decimal places as needed.)
(iii) The approximate percentage is (2) ______ the actual percentage.