Please help, I would appreciate an explanation on how you got the answer so I can understand it, being that I am so confused.
The Denver Post stated that 80% of all new products introduced in grocery stores fail (are taken off the market) within 2 years. A grocery store chain introduces 66 new products this year. What is the chance that more than 75% of these new products fail within 2 years?
1.Average?
2.SD?
3.The number of draws?
4. expected value of the percentage (EV%):
5.Enter the standard error of the percentage (SE%).
6.Enter the chance more than 75% of the new products introduced this year will fail within 2 years. Round to the nearest whole number.
To find the chance that more than 75% of the new products introduced this year will fail within 2 years, we need to use the concept of the binomial distribution. The binomial distribution is used to model the probability of a certain number of successes (in this case, product failures) in a fixed number of trials (the number of new products introduced).
To calculate the probability, we need a few inputs:
1. Average: The average probability of success on a single trial. In this case, the probability of failure is given as 80%, so the average probability of success (p) is 1 - 0.8 = 0.2.
2. SD (Standard Deviation): The standard deviation of the probability of success on a single trial. For a binomial distribution, the standard deviation (sd) is calculated as the square root of p(1-p).
sd = √(0.2 * 0.8) = √0.16 = 0.4
3. The number of draws: The number of new products introduced this year is 66.
4. Expected value of the percentage (EV%): This is calculated as the average multiplied by the number of draws.
EV% = 0.2 * 66 = 13.2
5. Standard error of the percentage (SE%): This is calculated as the standard deviation divided by the square root of the number of draws.
SE% = 0.4 / √66 ≈ 0.049
6. To find the chance that more than 75% of the new products fail within 2 years, we need to calculate the cumulative probability (from 75% to 100%) using the z-score.
Z-score = (75 - EV%) / SE% = (75 - 13.2) / 0.049 ≈ 133.9
Looking up the z-score in a standard normal distribution table, we find that the cumulative probability is very close to 1 (or 100%).
Therefore, the chance that more than 75% of the new products introduced this year will fail within 2 years is approximately 100%.