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 ( ) ?

(Round to five decimal places as? needed.)

Explain steps please

Answer 1

Let x be the number of correctly identifying the marriage status of a man in any given? photograph.

We are given that the sample distribution for this study is unimodal and symmetric and that the samples are collected randomly; also we are given p = 69% and n = 100

Therefore x follows normal distribution with mean = n*p = 0.69*100 and

standard deviation = here q =1-p , so s.d =

Therfore x follows normal distribution with mean = 69 and standard deviation = 4.6249

We are asked to find P( x >= 78 ) using normal approximation,

So first we need to do continuity correction for x by subtracting 0.5 from 78

Therefore P( x >=78-0.5) => P( x >=77.5)

First we have to find z score for x = 77.5

z = =   = 1.84

P( z >= 1.84)  

We have to find probability or area greater than 1.84 using normal table ( z score table )

So we need to look at the row 1.8 and across column 0.04 in the positive z score table .

On the z score table probabilities or area less than z are available, we got probability less than 1.84 is 0.9671

Or you can excel function =NORMSDIST(z) to find the probability less than z

So using excel function =NORMSDIST(1.84) we get the same probability 0.967116

But we are asked to find probability greater than 1.84 , therefore we need to subtract 0.967116 from 1

1 - 0.967116 = 0.03288

the probability a woman would correctly classify 78 or more of the? men is 0.03288