The heights of 1500 students are normally distributed with a mean of 176.5 centi
ID: 2908802 • Letter: T
Question
The heights of 1500 students are normally distributed with a mean of 176.5 centimeters and a standard deviation of 6.9 centimeters. Assuming that the heights are recorded to the nearest half-centimeter, how many of these students would be expected to have heights (a) less than 163.0 centimeters? (b) between 171.5 and 184.0 centimeters inclusive? (c) equal to 177.0 centimeters? (d) greater than or equal to 194.0 centimeters? Click here to view page 1 of the standard normal distribution table (a)student's) Round to the nearest whole number as needed.)Explanation / Answer
a) Frequency = 1500 * p(X < 163)
= 1500 * p(Z < 163 - 176.5/6.9)
= 1500 * p(Z < -1.96)
= 1500 * 0.025
= 37.5
Approximately 38
b) Frquency
1500 * p(171.5 < x < 184) = p(171.5 - 176.5/6.9 < Z < 184 - 176.5/6.9)
= 1500 * p(-0.72 < Z < 1.09)
= 1500 * 0.6264
= 940
c) frquency = 0
since probability of a particular real value is '0'
d) Frequency = 1500 * p(X > 194)
= 1500 * p(Z > 2.54)
= 1500 * 0.0055
= 8
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