Question

The heights, in inches, for 120 people (male and female) have been measured. The results are presented:

Download the data

Heights sample data:
65.14	66.74	65.37	65.08	69.62	69.34	70.32	62.38	67.77	64.1	65.43	63.21
66.74	62.22	68.76	67.67	68.29	66.62	66.74	66.8	63.06	70.33	67.36	64.78
67.2	68	66.09	67.81	67.58	69.13	65.06	62.91	64.05	66.49	60.33	68.98
65.57	63.88	64.62	66.27	68.32	61.34	63.95	71.76	63.1	70.3	64.89	66.74
67.77	64.22	69.18	71.19	67.43	63.7	69.87	70.1	65.07	64.84	64.74	67.41
70.81	66.66	64.32	60.07	65.47	64.01	71.61	73.78	68.28	64.98	66.87	64.29
67.66	69.04	65.39	65.76	68.01	64.74	64.52	67.46	66.41	72.48	66.79	68.37
65.62	64.78	63.42	61.04	61.67	65.21	65.27	67.57	65.21	68.98	56.51	62.66
67.96	61.99	65.04	62.05	64.98	63.09	67.09	70.27	63.4	59.78	66.43	67.58
70.54	65.69	66.58	68.38	63.86	62.9	65.65	67.49	73.29	67.1	65.23	62.82

a)Calculate the mean and standard deviation for the sample. Give your answers to 2 decimal places.

sample mean =

sample standard deviation =

b)Find the proportion of heights that are within 1 standard deviation of the sample mean and also the proportion that are within 2 standard deviations of the sample mean. Use the unrounded values for the mean and standard deviation when doing this calculation. Give your answers as decimals to 2 decimal places.

Proportion of heights within 1 standard deviation of the mean =

Proportion of heights within 2 standard deviations of the mean =

c)Select the appropriate description for the data:

the data are APPROXIMATELY normal
the data are CLEARLY not normal

d)Calculate the standardized value for the value 70. Note that, for a value x within a sample that is approximately distributed as N(x,s), a standardized value can be calculated as z = (x - x) / s

standardized value (to 2 decimal places) for the value 70 =

e)Calculate the probability that a standard normal random variable Z takes a values less than the standardized value calculated in part d). Give your answer as a decimal to 4 decimal places.

Probability Z less than standardized value =

f)Find the proportion of values in the sample that are less than or equal to 70. Give you answer as a decimal to 2 decimal places.

Proportion of values less than or equal to 70 =

Answer 1

for the question C

from Shapiro-Wilk normality test as the probability value greater than 0.05 we accept that the sample is APPROXIMATELY normal