Final answer:
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.