Question

Suppose you randomly guess on every question of a 20 question True/False test. Let x = number of questions that you answer correctly. Although values of x are whole numbers, x has an approximately normal distribution with mean = 10 and standard deviation = 2.2. What is the probability that you would get at least 12 questions correct?

Answer 1

Answer:

18.14% probability that you would get at least 12 questions correct.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 10, \sigma = 2.2$

What is the probability that you would get at least 12 questions correct?

This is 1 subtracted by the pvalue of Z when X = 12. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{12 - 10}{2.2}$

$Z = 0.91$

$Z = 0.91$ has a pvalue of 0.8186.

So there is a 1-0.8186 = 0.1814 = 18.14% probability that you would get at least 12 questions correct.