1- An oil change shop advertised to change oil within 15 minutes. Based on the data collected on a typical day, what is the probability that the oil change will take 15 minutes or less time? Based on the data, do you think the business claim is valid? Explain why or why not, and be sure to cite the appropriate principles from your text to support any claims or assertions made in your response.

Class Interval Frequency

6 to 10 minutes 3

11 to 15 minutes 8

16 to 20 minutes 6

21 to 25 minutes2

More than 25 Minutes 1

As per the data, the number of times the oil change has taken 15 minutes or less time = 3 + 8 = 11
Total frequency = 3 + 8 + 6 + 2 + 1 = 20
 Probability that the oil change will take 15 minutes or less time = 11/20 = 0.55
The above probability value is too high. This means it is unlikely that the oil change will happen in 15 minutes or less time. The claim is not valid.
[However, if we conduct a t- test (hypothesis test) with α = 0.10, we will have insufficient evidence to reject the claim that the oil change takes 15 minutes or less. This means the claim that the oil change happens in 15 minutes or less is valid. If this question is from hypothesis testing, I can further provide detailed calculations for the above result.]

2- What are the characteristics of standard normal distribution? The HR department of an organization collects data on employees’ age, salary, level of education, gender, and ethnicity. Which data do you think is more likely to follow normal distribution? Explain why. Make sure you support any claims or assertions with the relevant principles from your text.

The standard normal distribution is the normal distribution with a mean of 0 and a variance of 1.
The main characteristics of the standard normal distribution are:
(a) The distribution is bell shaped
(b) The normal probability density function is symmetric about its mean value.
(c) The mean, median and mode of the distribution are all equal.
(d) The inflection points (The points where the curve changes its concavity) of the curve occur at one standard deviation away from the mean.
Of the data collected, we can expect Salary to be normally distributed. If the organization has employees of all age groups, even Age can be a normal variate. The other variables such as level of education, gender and ethnicity are categorical and not numerical. As such we can’t fit a normal distribution to these data.