Example 73

Example 73:  A study completed in 2011 looked at the effects of self-control on relationship infidelity.  The hypothesis under investigation was that people have a limited reserve of self-control, so when exercising it in one area (for example, when trying to maintain a diet), they might be less able to discipline themselves in other areas.  In the study, participants currently involved in an exclusive romantic relationship and depleted of self-control by resisting cookies were more likely to make a coffee date with and disclose their personal phone number to a confederate than their non-depleted counterparts. There was no difference in self-reported likelihood of engaging in either behavior based on condition. Those in the depletion condition self-reported the same likelihood of accepting a coffee date and giving a personal phone number as those not depleted, yet when tempted in the study, the depleted group did end up cheating at a significantly higher rate than the not depleted group.  The depleted group accepted an invitation to go on a date (and gave out their number) in 74% of the cases (verses only 31% for the not depleted group).  Using the 74% from the study as the rate of infidelity, find the mean and standard deviation for the number of people in a committed relationship, out of a group of 49, that would commit infidelity while in a depleted state.  Would it be unusual for less than 26 people in the group to be unfaithful?