Probability urgent help please

[trendsetter123ftw]

 A supermarket claims that 90% of all the strawberries it sells are regular.

One of the customers collects a random sample of 51 strawberries after buying two large packets and found that there are 47 regular strawberries in the sample


a.       a. Find the exact expected value and standard deviation, of the sampling distribution of the proportion of regular strawberries in his sample

Is the expected value 0.9 or 47/51? Please explain why


When calculating the standard deviation would we use 0.9 or 47/51? Please explain why


Find the probability that 85% of the strawberries in his sample are regular

85% of 51 = 43.35, which rounds up to 44, but do we use 0.9 or 47/51? Please explain why


Use the normal distribution with the expected value and standard deviation from part a. to find the approximate probability that at least 80% of the strawberries in his sample are regular. Give your answer correct to three decimal places

Since it says to use the normal distribution is the expected value 0.9 * 51 = 45.9 and the standard deviation the square root (45.9*0.1)?


Find the z value that gives a 98% confidence interval. How would you convert confidence intervals to z values?

Find the 98% confidence interval for the proportion of reagular strawberries sold by the supermarket

Do we use 0.9 or 47/51? Please explain why


As you can probably tell, I’m confused with this sampling topic in probability and would appreciate any help. Thanks

[S_R_K]

In a very broad sense, there are two "perspectives" you can take when dealing with sampling.

1. You know the population distribution (ie. the proportion of individuals in the entire population with a given characteristic), and you want to calculate the probability that a random sample will have a given proportion of individuals with that characteristic. These are the questions where you are asked to find the mean / standard deviation of the distribution of sampling proportions. For these, use the proportion within the population - in this case, 0.9.

2. You know the proportion of individuals with a given characteristic in a random sample, and you want use that sample to infer a reasonable estimate of the proportion of individuals with that characteristic in the entire population. These are the questions where you are asked to find a confidence interval for the population proportion. For these, use the proportion within the sample - in this case 47/51.