Question

The results of a study showed that heterosexual​ women, during​ ovulation, were significantly better at correctly identifying the marriage status of a man from a photograph of his face than women who were not ovulating. Near​ ovulation, on average women correctly identified the marriage status of about 69 ​% of the 100 men shown to them. Assume that the sample distribution for this study is unimodal and symmetric and that the samples are collected randomly. If this is the probability of correctly identifying the marriage status of a man in any given​ photograph, what is the probability a woman would correctly classify 78 or more of the​ men? The probability is nothing .  

Answer 1

Let X denote the number of men who would be correctly classified by a randomly selected women near ovulation

n = 100, p = 0.69

np = 69 , np(1 - p) = 21.39

Thus, X can be approximated to Normal distribution with Mean = 69 and standard deviation = √21.39 = 4.625

The probability a woman would correctly classify 78 or more of the men = P(X ≥ 78)

Using correction of continuity, the required probability

= P(X > 77.5)

= P{Z > (77.5 - 69)/4.625}

= P(Z > 1.838)

= 0.0331