Question

Suppose the company that makes Sweet Tarts states that the proportion of orange candies in a bag is 27%. Give the standard deviation for the distribution of orange Sweet Tarts in a bag of 326. In your answer, include the probability of more than 85 orange Sweet Tarts in a bag of 326.

Answer 1

The standard deviation for the distribution of orange Sweet Tarts in a bag of 326 is approximately 9.39 candies. The probability of more than 85 orange Sweet Tarts in a bag of 326 is approximately 0.1562.

Step-by-step explanation:

To find the standard deviation, we need to use the formula:

standard deviation = sqrt(n * p * (1-p))

where n is the sample size (in this case, 326) and p is the proportion of orange candies (0.27).

Substituting the values into the formula, we get:

standard deviation = sqrt(326 * 0.27 * (1-0.27))

standard deviation = sqrt(88.2388)

standard deviation ≈ 9.39 candies.

To find the probability of more than 85 orange Sweet Tarts in a bag of 326, we can use z-score and the standard normal distribution table. We calculate the z-score as:

z = (x - mean) / standard deviation

where x is the threshold (85), mean is n * p (326 * 0.27), and standard deviation is 9.39.

Substituting the values into the formula, we get:

z = (85 - (326 * 0.27)) / 9.39

z ≈ 1.009

Using the standard normal distribution table, the probability of more than 85 orange Sweet Tarts is approximately 0.1562.