Question

A recent poll has suggested that 67 % of Canadians will be spending money - decorations, halloween treats, etc. - to celebrate Halloween this year. 25 Canadians are randomly chosen, and the number that will be spending money to celebrate Halloween is to be counted. This count is represented by the random variable X .

Part (c) How many of the 25-Canadians randomly chosen would you expect to indicate they will be spending money to celebrate Halloween? Compute the standard deviation as well.

E ( X ) = μ X = (use two decimals in your answer)

S D ( X ) = σ X = (use two decimals in your answer)

Part (d) Compute the probability that the 12-th Canadian random chosen is the 9-th to say they will be spending money to celebrate Halloween. (use four decimals in your answer)

Answer 1

To find the expected number of Canadians who would spend money to celebrate Halloween, you can multiply the probability of spending money by the sample size. The standard deviation can be calculated using a formula. The probability of a specific order occurring can be found using the probability of success in each trial.

Step-by-step explanation:

To find the number of Canadians who would be expected to spend money to celebrate Halloween, we can use the probability distribution of the random variable X.

The mean (expected value) of X can be calculated by multiplying the probability of spending money (0.67) by the total number of Canadians (25).

So, E(X) = 0.67 * 25 = 16.75. Therefore, we would expect approximately 17 Canadians out of the 25 randomly chosen to indicate they will be spending money to celebrate Halloween.

To compute the standard deviation (SD) of X, we need to use the formula: SD(X) = sqrt(N * p * (1-p)), where N is the sample size (25) and p is the probability of success (0.67).

Plugging in the values, SD(X) = sqrt(25 * 0.67 * (1-0.67)) = sqrt(8.366475) ≈ 2.89. Therefore, the standard deviation of X is approximately 2.89.

For the probability that the 12th Canadian randomly chosen is the 9th to say they will be spending money to celebrate Halloween, we know that the probability of an individual Canadian saying they will be spending money is 0.67.

Therefore, the probability of this specific order occurring is (0.67)^8 * (1-0.67)*(0.67)^2 ≈ 0.0237.