Answer:
Step-by-step explanation:
-For a known standard deviation, the sample size for a desired margin of error is calculated using the formula:
Where:
We substitute our given values to calculate the sample size:
Hence, the smallest desired sample size is 23
Answer:
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Solution to the problem
Let X the random variable of interest, on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
The mean for the binomial distribution is given by:
And the variance is given by:
And the deviation is just the square root of the variance so we got: