Question 1197112: In a survey of nursing students pursuing a master's degree, 75 percent stated
that they expect to be promoted to a higher position within one month after
receiving the degree. If this percentage holds for the entire population, find,
for a sample of 15, the probability that the number expecting a promotion
within a month after receiving their degree is: 4pts each
(a) At last seven.
(b) No more than five.
(c) Between six and nine, inclusive.
(d) How many nurses would expect to see a proportion in the month after graduation?
Please explian option (d) with formula
Answer by ikleyn(52780)   (Show Source):
You can put this solution on YOUR website! .
In a survey of nursing students pursuing a master's degree, 75 percent stated
that they expect to be promoted to a higher position within one month after
receiving the degree. If this percentage holds for the entire population, find,
for a sample of 15, the probability that the number expecting a promotion
within a month after receiving their degree is: 4pts each
(a) At  least seven.
(b) No more than five.
(c) Between six and nine, inclusive.
(d) How many nurses would expect to see a proportion in the month after graduation?
Please explain option (d) with formula
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It is typical problem on binomial distribution.
Number of trials is 15. The probability of individual success is 0.75 for each trial.
There are standard formulas to calculate everything and answer your questions.
You may find these formulas in your textbook.
The goal of this problem is not to teach you to use these standard formulas,
but, instead, to learn the strategy on HOW TO do it, in general.
THEREFORE, instead of using these formulas, I will use free of charge online calculator
at this web-site https://stattrek.com/online-calculator/binomial.aspx
It provides nice instructions and a convenient input and output for all relevant options/cases.
So for your questions
(a) P = P(n=15; k >= 7; p=0.75) = 0.99581. ANSWER
(b) P = P(n=15; k <= 5; p=0.75) = 0.00079. ANSWER
(c) P = P(n=15; k <= 9; p=0.75) - P(n=15; k < 6; p=0.75) = 0.14837 - 0.00079 = 0.14758. ANSWER
(d) This question is about the Mathematical expectation.
The formula for it is E = np for the binomial distribution,
which gives in your case E = 15*0.75 = 11.25. ANSWER
Notice that it is consistent with the common sense: 75% of 15 is exactly and precisely 11.25.
Solved, with full explanations.
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If you want to see many similar (or different) solved problems, look into the lessons
- Simple and simplest probability problems on Binomial distribution
- Typical binomial distribution probability problems
- How to calculate Binomial probabilities with Technology (using MS Excel)
- Solving problems on Binomial distribution with Technology (using MS Excel)
- Solving problems on Binomial distribution with Technology (using online solver)
in this site.
After reading these lessons, you will be able to solve such problems on your own,
which is your PRIMARY MAJOR GOAL visiting this forum (I believe).
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