Normal distribution A and I exam question 2021

Video Comprehension Questions for Year 12 Students
1. What is the relationship between variance and standard deviation in a normal distribution?
a. Variance is the square of the standard deviation.
b. Variance is the cube of the standard deviation.
c. Variance is the square root of the standard deviation.
d. Variance is half of the standard deviation.

2. In the context of male Persian cats' weights, what does a variance of 0.5 squared imply?
a. The standard deviation is 0.5.
b. The standard deviation is 1.
c. The mean weight is 0.5 kilograms.
d. The mean weight is 0.25 kilograms.

3. What is the first step mentioned in the video for solving a normal distribution question?
a. Find the median of the data.
b. Calculate the mode of the distribution.
c. Sketch a bell curve.
d. Determine the range of the data.

4. How is the probability of male Persian cats weighing between 5.5 and 6.5 calculated?
a. Using the normal distribution formula.
b. By multiplying the mean and the standard deviation.
c. By dividing the range by the mean weight.
d. By using the calculator's normalcdf function.

5. When determining the expected number of cats weighing less than 5.3, what should be multiplied by the probability?
a. The standard deviation.
b. The variance.
c. The mean.
d. The size of the cat population.

6. What type of question is Question D in the video related to normal distribution?
a. Direct question.
b. Inverse question.
c. Probability question.
d. Range question.

7. How is the value of x estimated in the context of cats weighing more than x kilograms?
a. By finding the probability of cats weighing less than x.
b. By subtracting the known weights from x.
c. Through the inverse normal distribution calculation.
d. By multiplying the weights by the standard deviation.

8. Which step is essential in converting a probability into the expected number of cats?
a. Rounding to the nearest whole number.
b. Multiplying the probability by the total population size.
c. Dividing the population size by the standard deviation.
d. Taking the square root of the probability.

9. What is the significance of focusing on the left-hand side of the graph in an inverse normal question?
a. It indicates smaller values.
b. It represents the max value.
c. It shows the mean weight.
d. It suggests outliers in the data.

10. What is the benefit of using inverse normal calculation when estimating the value of x in the problem?
a. It provides a precise range for x.
b. It guarantees a whole number solution.
c. It avoids rounding errors.
d. It simplifies the calculation process.

Answer Key:
a (00:00:46)
a (00:01:20)
c (00:01:35)
d (00:02:41)
d (00:04:33)
b (00:06:23)
c (00:07:11)
b (00:06:23)
a (00:09:41)
c (00:11:32)