Question

*Please show excel function*

What is the probability that a student will be over 60 inches tall? (assume that the data are normally distributed with the population standard deviation =4.25)

Height in inches

Student 1	64
2	63
3	63
4	63
5	63
6	65
7	66
8	66
9	67
10	68
11	68
12	66
13	68
14	78
15	76
16	75
17	75
18	73
19	73
20	72
21	70
22	70
23	70
24	70
25	69
26	69

Answer 1

	Values ( X )	$\Sigma (X_{i} - \bar{X})^{2}$
	64	23.4857
	63	34.1781
	63	34.1781
	63	34.1781
	63	34.1781
	65	14.7933
	66	8.1009
	66	8.1009
	67	3.4085
	68	0.7161
	68	0.7161
	66	8.1009
	68	0.7161
	78	83.7921
	76	51.1769
	75	37.8693
	75	37.8693
	73	17.2541
	73	17.2541
	72	9.9465
	70	1.3313
	70	1.3313
	70	1.3313
	70	1.3313
	69	0.0237
	69	0.0237
Total	1790	465.3858

$Mean \bar{X} = \Sigma X_{i} / n$

$\bar{X} = 1790 / 26 = 68.8462$

$X \sim N ( \mu = 68.8462 , \sigma = 4.25 )$

P ( X > 60 ) = 1 - P ( X < 60 )

Standardizing the value

$Z = ( X - \mu ) / \sigma$

Z = ( 60 - 68.8462 ) / 4.25

Z = -2.08

$P ( ( X - \mu ) / \sigma ) > ( 60 - 68.8462 ) / 4.25 )$

P ( Z > -2.08 )

P ( X > 60 ) = 1 - P ( Z < -2.08 )

P ( X > 60 ) = 1 - 0.0188

P ( X > 60 ) = 0.9812

Excel function   1-NORMSDIST( Z = - 2.08 ).