Given that a sample of 36 women is selected, the probability that the mean is between 264 days and 266 days will be found as follows: the std deviation of the sample will be: σ/√n plugging the values we obtain: 15/√36 =15/6 =2.5 hence the z-score when x=264 will be: z=(264-264)/2.5 z=0 thus: P(x<264)=P(z<0)=0.5
the z-score when x=266 will be: z=(266-264)/2.5 z=0.8 hence P(x<266)=P(z<0.8)=0.7881 thus P(264<x<266)=P(0.5<z<0.7881) =0.7881-0.5 =0.2881
