The table below shows arelative-frequency distribution for the heights of female students at a midwestern college. The heights are approximately normally distributed with mean 64.5 inches and standard deviation 1.9 inches.

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Height

(inches)

Frequency

f

Relative frequency

60An arrow points to the left.

<

61

3

0.0106

61An arrow points to the left.

<

62

9

0.0317

62An arrow points to the left.

<

63

25

0.0880

63An arrow points to the left.

<

64

64

0.2254

64An arrow points to the left.

<

65

86

0.3028

65An arrow points to the left.

<

66

64

0.2254

66An arrow points to the left.

<

67

25

0.0880

67An arrow points to the left.

<

68

6

0.0211

68An arrow points to the left.

<

69

2

0.0070

284

1.0000

Use a normal distribution with =64.5 and =1.9 to approximate the percentage of these students having heights within any specified range. In eachpart, (i)obtain the exact percentage from thetable, (ii)use the normal distribution to approximate thepercentage, 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

8.80

8.80%.

(Type an integer or adecimal.)

(ii) The normal distribution approximates the percentage of female students with heights between 62 and 63 inches to be

nothing

%.

(Round to two decimal places asneeded.)