Question

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

Heights sample data:
71.06	69.71	63.48	69.89	64.43	64.92	70.55	61.87	65.81	66.47	69.99	68.25
65.7	58.46	66.96	69.29	67.45	67.71	66.95	67.57	70.9	64.51	66.43	70.96
62.9	67.52	68.09	64.33	63.46	69.68	66.58	62.48	67.22	64.59	63.21	63.94
64.35	66.22	64.68	62.73	66.82	67.33	66.02	65.9	66.43	71.44	70.64	66.49
68.91	64.8	61.65	64.2	66.39	69.39	63.04	69.26	72.61	61.03	69.71	67.38
65.64	72.74	69.95	63.95	57.79	66.26	59.26	69.72	65.12	63.73	66.25	72.65
68.75	62.95	65.12	68.25	68.34	64.49	67.27	66.96	72.13	63.68	67.15	63.75
71.24	69.49	67.05	68.02	67.14	67.07	66.1	66.56	66.46	60.98	69.94	70.27
65.85	65.28	69.91	71.55	70.05	65.86	68.69	68.72	69.52	64.71	64.79	66.28
68.73	64.86	67.39	65.13	66.79	66.14	69.57	64.09	70.31	62.62	60.9	67.41

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