The ACT is a standardized college admissions test used in the United States. The four multi-part questions in this assessment all involve simulating some ACT test scores and answering probability questions about them. For the three year period 2016-2018, ACT standardized test scores were approximately normally distributed with a mean of 20.9 and standard deviation of 5.7. (Real ACT scores are integers between 1 and 36, but we will ignore this detail and use continuous values instead.)
First we'll simulate an ACT test score dataset and answer some questions about it.
Set the seed to 16, then use rnorm() to generate a normal distribution of 10000 tests with a mean of 20.9 and standard deviation of 5.7. Save these values as act_scores. You'll be using this dataset throughout these four multi-part questions.
A. In act-sources, what is the probability of an ACT score greater than 30?B. In act-sources, what is the probability of an ACT score less than or equal to 10?