In a recent​ year, the scores for the reading portion of a test were normally​ distributed, with a mean of 22.3 and a standard deviation of 5.8. Complete parts​ (a) through​ (d) below.​(a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 16. The probability of a student scoring less than 16 is nothing.​(Round to four decimal places as​ needed.)​(b) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is between 18.7 and 25.9. The probability of a student scoring between 18.7 and 25.9 is nothing.​(Round to four decimal places as​ needed.)​(c) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is more than 34.2. The probability of a student scoring more than 34.2 is nothing.​(Round to four decimal places as​ needed.)​(d) Identify any unusual events. Explain your reasoning. Choose the correct answer below. A. The event in part (c) is unusual because its probability is less than 0.05. B. The event in part (a) is unusual because its probability is less than 0.05. C. None of the events are unusual because all the probabilities are greater than 0.05. D. The events in parts (a) and (b) are unusual because its probabilities are less than 0.05.

Q: Find the probability that a randomly selected high school student who took the reading portion of…

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Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.