Probabilities are used to determine the chances of events
The given parameters are:
- Sample size: n = 20
- Proportion: p = 85%
Using the binomial probability formula, we have:
So, the equation becomes
This gives
Express as percentage
Hence, the probability that 11 out of the 20 would graduate is 0.11%
<h3>(b) To what extent do you think the university’s claim is true?</h3>The probability 0.11% is less than 50%.
Hence, the extent that the university’s claim is true is very low
<h3>(c) What is the probability that all 20 would graduate? </h3>Using the binomial probability formula, we have:
So, the equation becomes
This gives
Express as percentage
Hence, the probability that all 20 would graduate is 3.88%
<h3>(d) The mean and the standard deviation</h3>The mean is calculated as:
So, we have:
The standard deviation is calculated as:
So, we have:
Hence, the mean and the standard deviation are 17 and 2.55, respectively.
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