# In a poll men and women were asked"When someone yelled or snapped at you at work

In a poll men and women were asked"When someone yelled or snapped at you at work, how did you want to respond Twenty percent of the women in the survey said that they felt like crying (TimeApril 4, 2011) Suppose that this result is true for the current population of women employees. Arandom sample of 24 women employees is selectedUse the binomial probabilities table or technology to find the probability that the number of women employees in this sample of 24 who will hold the above opinion in response to the said question is

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Step 1
Given that :
Binomial Probability $$\displaystyle=^{{{n}}}{C}_{{{x}}}\times{\left({p}\right)}^{{{x}}}\times{\left({q}\right)}^{{{n}-{x}}}$$
where $$\displaystyle{n}=$$ number of trials and x is the number of successes.
Here $$\displaystyle{n}={24},{p}={0.2},{q}={1}-{p}={0.8}$$
Step 2
(a) P(at least 5) $$\displaystyle={P}{\left({5}\right)}+{P}{\left({6}\right)}+\ldots..+{P}{\left({25}\right)}$$
Using Technology P(At least 5) $$\displaystyle={0.5401}$$
(b) $$\displaystyle{P}{\left({5}\to{7}\right)}={P}{\left({5}\right)}+{P}{\left({6}\right)}+{P}{\left({7}\right)}={0.1960}+{0.1551}+{0.0997}={0.4508}$$
(c) $$\displaystyle{P}{\left(\text{At most}\ {6}\right)}={P}{\left({0}\right)}+{P}{\left({1}\right)}+\ldots.+{P}{\left({6}\right)}={0.8111}$$