Final answer:
The random variable X represents the number of strawberry candies selected from a special bag containing a mix of candies. X can take values from 0 to 20, and the hypergeometric distribution is used to calculate probabilities such as P(X>18) and P(X=3), as well as expected value E[X] and variance Var[X].
Step-by-step explanation:
The random variable X represents the number of strawberry candies that will be selected when picking 35 pieces of candy at random from a bag containing 20 strawberries, 20 cherry, and 10 orange candies. The following responses address each part of the question:
- (a) Error: This part of the question appears to be incomplete or contains a typo and cannot be answered as presented.
- (b) The possible values for X are from 0 to 20, inclusive.
- (c) To find the chance that more than 18 strawberry-flavored candies are chosen, P(X>18), we must use a hypergeometric distribution because the draws are without replacement.
- (d) The chance that exactly 3 strawberry-flavored candies are chosen, P(X=3), would require calculating the hypergeometric probability for X=3.
- (e) The expected number of strawberry-flavored candies to be chosen, E[X], can be found by multiplying the proportion of strawberry candies in the bag by the sample size.
- (f) To determine Var[X], the variance of X, apply the formula for the variance of a hypergeometric distribution.