Siddhant K. answered • 06/29/23
Student Teacher! Patient and Thorough
b) The shape of the histogram for this frequency table would be right-skewed. This is because the majority of the probabilities are concentrated on the left side of the distribution, with a long tail extending towards the right.
c) To find the mean number of days to fix defects, we need to multiply each number of days by its corresponding probability, and then sum up the results. Using the provided table:
Mean = (1 * 0.235) + (2 * 0.108) + (3 * 0.103) + ... + (18 * 0.001)
Calculating this expression yields the mean number of days to fix defects.
d) To find the standard deviation for the number of days to fix defects, we need to calculate the variance first. The variance is the sum of the squares of the differences between each number of days and the mean, multiplied by their corresponding probabilities. Then, taking the square root of the variance gives us the standard deviation. The formula for variance is:
Variance = (Σ [(x - mean)^2 * probability])
Once the variance is obtained, the standard deviation can be calculated as the square root of the variance.
e) To find the probability that it will take at least 15 days to fix the defect, we need to sum up the probabilities for all the days equal to or greater than 15. From the given table, this would involve adding the probabilities for 15, 16, 17, and 18 days.
f) Whether it is unusual for it to take 15 days to fix a defect on a pair of eyeglasses depends on the context and the specific criteria used to define "unusual." Generally, if the probability of an event is low (e.g., less than 5%), it can be considered uncommon or unusual. Therefore, by comparing the probability associated with 15 days (as calculated in part e) to a predetermined threshold (such as 5%), we can determine if it is unusual in this case.
