Cumulative Chapter Six Evaluation roblem 1 Acording to a study done by De Anza s

Question

Cumulative Chapter Six Evaluation roblem 1 Acording to a study done by De Anza students, te height for Asian admales is normaly dtitutad with an average of 69 idesrda standard deviation of 3.5 inches. Suppose one Asian adult male is randomly chosen. Let X- height of the individual. In each appropriate box you are to enter either a rational number in "p/" format or a decimal value accurate to the nearest 0.01 (.3)x 3.5 s(35) The probability that the person is between 65 and 69 ides talis Ft65SXS 69) (35) The middle 40% of heights fall between what two values? and a=

Explanation / Answer

We know that, 68% (approx) of the results fall in +- 1 standard deviation

14% in +- 2 standard devation each

2% in +- 3 standard deviation each

a). since the p=0.3 the standard deviation should be +-2. Hence, (62,65.5) or (72.5,76)

b). The probability is corresponding to 1SD, and thus the answer is 0.34

c). The middle 40% should be taken as (40/68 * 3.5) = 2.05 both towards the right and left of 69 (67,71)

We multiply 40/68 with 3.5 in order to "trim" the standard deviation and equate it to the middle 40% as has been asked, as against middle 68% as is usually assumed.

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