Introduction to Statistics
Customer satisfaction is an example of what type of variable?
Ordinal level
In Steve's data, the mean is larger than the median. What does this tell you about the distribution?
The distribution is positively skewed (right-skewed).
If two events are independent, how do you find the probability of their joint occurrence?
Multiply their probabilities together
What are the characteristics of a discrete random variable?
Sum of probabilities of all possible outcomes is 1
The probability of a particular outcome is between 0 and 1
All outcomes are mutually exclusive
What type of variable is used to measure the time it takes to travel to Ngee Ann?
Quantitative, continuous or ratio level
Patricia wants to compare the variation between two samples involving different quantitative variables with different measurement scales. What method would be best for this comparison?
Use a coefficient of variation
If P(A)=0.4P(A) = 0.4P(A)=0.4, P(B)=0.7P(B) = 0.7P(B)=0.7, and P(A and B)=0.25, what can you conclude about the events A and B?
The events are non-mutually exclusive.
A wine sales business has found that, on average, each customer buys a rare bottle of wine with a probability of 0.04. If the store serves 60 customers in a day, what is the probability that exactly 2 customers will buy a rare bottle of wine?
0.2613 or 26.13%
Steve, a personal chef, analysed a sample of 25 dishes from his menu to record their calorie content. Based on this data, how many classes are recommended for constructing a frequency table?
Five classes
Sarah claims, "Variance is always greater than the standard deviation because variance is the square of the standard deviation." Tom disagrees, saying, "The standard deviation can be larger than the variance." Who is correct, and why?
Tom is correct
Jessica sources 400 vinyl records each month from Golf Co., Mitski Inc., and Twilight Co. She reviews the defective records from these suppliers to make an informed business decision. Given the following data, what is the probability that a random record is defective?
Suppliers, Defective Rate (%), Order Quantity
Golf Co. (2.3) (150)
Mitski Inc. (1.1) (200)
Twilight Co. (3.1) (50)
0.018 or 1.8%
80 registrants have signed up for the Art Festive event. Each registrant is required to choose one time slot to attend from the options: 9am, 11am, 1pm, or 3pm. Is this scenario a binomial experiment? Explain why.
No
Given Steve's sample data of calorie content from 25 dishes:
245, 292, 177, 283, 256, 289, 253, 202, 293, 220, 277, 220, 263, 164, 201, 207, 270, 188, 220, 234, 159, 231, 270, 239, 198.
What class interval should be used to create a frequency table?
Interval length = (Max. – Min.)/ Classes = (293 – 159)/5 = 26.8 = 27
Calculate the mean and median of Steve's data set:
245, 292, 177, 283, 256, 289, 253, 202, 293, 220, 277, 220, 263, 164, 201, 207, 270, 188, 220, 234, 159, 231, 270, 239, 198.
Mean: 234.04
Median: 234
Jessica sources 400 vinyl records each month from Golf Co., Mitski Inc., and Twilight Co. She reviews the defective records from these suppliers to make an informed business decision. What is the probability that a record was produced by Mitski Inc., given that it was defective?
Suppliers, Defective Rate (%), Order Quantity
Golf Co. (2.3) (150)
Mitski Inc. (1.1) (200)
Twilight Co. (3.1) (50)
0.3056 or 30.56%
The probability of a baker accidentally making a mistake on a recipe is 0.05. What is the probability that the baker does not make a mistake in 15 recipes?
0.4633 or 46.33%
Organize the following calorie data into a frequency distribution table:
245, 292, 177, 283, 256, 289, 253, 202, 293, 220, 277, 220, 263, 164, 201, 207, 270, 188, 220, 234, 159, 231, 270, 239, 198.
Interval Frequency
159–186 (3)
187–214 (5)
215–242 (7)
243–270 (5)
271–297 (5)
Using the frequency table constructed earlier, calculate the mean, median, and mode of the data.
Mean: 232.88
Median: 238.14
Mode: 228.5
Jessica sources 400 vinyl records each month from Golf Co., Mitski Inc., and Twilight Co. She reviews the defective records from these suppliers to make an informed business decision. What is the probability that a record was produced by Mitski Inc. or Twilight Co., given that it was defective?
Suppliers, Defective Rate (%), Order Quantity
Golf Co. (2.3) (150)
Mitski Inc. (1.1) (200)
Twilight Co. (3.1) (50)
0.5208 or 52.08%
Customers arrive at a bakery at random at an average rate of 8 per hour. What is the probability that, during any 80-minute period, the number of customers arriving at the bakery is more than 1?
0.9997 or 99.97%