Reference no: EM132463511
A group of 110 students sat an aptitude test, their resulting scores are presented:
54, 55, 57, 57, 57, 58, 58, 58, 59, 59, 59, 59, 60, 60, 60, 61, 61, 62, 62, 62, 62, 62, 63, 63, 63, 63, 64, 64, 65, 65,65, 65, 65, 65, 66, 66, 66, 66, 66, 66, 67, 67, 67, 67, 67, 67, 67, 67, 68, 68, 68, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 70, 70, 70, 70, 70, 71, 71, 71, 71, 71, 72, 72, 72, 72, 72 72, 72, 72, 72, 72, 73, 73, 73, 74, 74, 74, 74, 75, 75, 75, 76, 77, 77, 77, 78, 78, 78, 78, 79, 79, 79, 79, 79, 79, 81, 84, 84, 91
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 scores 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 scores within 1 standard deviation of the mean =
Proportion of scores 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 sample value 60. 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) / standardized value (to 2 decimal places) for the sample value 60 =
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 60. Give you answer as a decimal to 2 decimal places.
Proportion of values less than 60 =