Question 12(c) | BetaMath

Question 12(c)

A charity employs a worker to collect donations. There is a $0.31$ chance that when the charity worker talks to someone a donation is made to the charity.

Each day the charity worker must talk to exactly $100$ people.

Use the standard normal distribution and the information on page 13 to approximate the probability that, on a particular day, at least $35$ % of the people talked to made a donation.

Solution

We can approximate the binominal distribution as a normal distribution with mean $\mu$ and standard deviation $\sigma$ .

The mean of a binomial distribution with $N$ samples and probability of success $p$ is given by the equation $\mu = Np$ so we can use this as the mean for our approxaimteion.

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