1. [1pt: 0.25pts each] Research from a big private university show that 7 out of
ID: 3352549 • Letter: 1
Question
1. [1pt: 0.25pts each] Research from a big private university show that 7 out of 10 graduating seniors completed the major they intended when they enrolled at the school. What is the probability that
a particular student completed her/his intended major?
two different randomly selected students both completed their intended major?
two different randomly selected students completed a different major than the one they intended?
one randomly selected student completed his/her intended major and another randomly selected student did not?
2. [1.5pts: 0.25pts each] A student taking a midterm exam in Ancient History comes to two questions pertaining to a lecture that he missed, and so he decides to take a random guess on both questions. One question is true-false and the other is multiple choice with four possible answers. What is the probability of guessing
the correct answer to the true/false question?
the correct answer to the multiple choice question?
the correct answers to both the true/false question and the multiple choice question?
the incorrect answers to both the true/false question and the multiple choice question?
the correct answer to the true/false question and an incorrect answer to the multiple choice question?
the incorrect answer to the true/false question and the correct answer to the multiple choice question?
3. [2pts: 0.25 pts each for a through d; 0.25pts for each empty box in the table] The table below shows a random sample of musicians and how they learned to play their instruments. Complete the highlighted cells of the table and answer the following questions.
How learned
Gender
Self-taught
Learned in school
Private instruction
TOTAL
Female
12
38
72
Male
58
TOTAL
31
62
37
130
What is the probability of randomly selecting a musician who is female?
What is the probability of randomly selecting a musician who is a male AND had private instruction?
What is the probability of randomly selecting a musician is a female OR one that is self-taught?
Are the events “being a female musician” and “learning music in school” independent events?
4. [1.5pts: 0.25pts each] The Superior Test of Achievement (STA) is standardized to be normally distributed with a mean = 500 and a standard deviation = 100. What percentage of STA scores falls
between 500 and 600?
between 400 and 600?
between 500 and 700?
between 300 and 700?
above 600?
below 300?
5. [4 pts: 0.25 pts each for a through h; 0.50 pts each for i through l,] Suppose that a principal of a local high school tracks the number of minutes his students spend texting on a given school day. He finds that the distribution of minutes spent texting is roughly normal with a mean of 60 and a standard deviation of 20. Determine:
the percentage of students texting for more than 90 minutes.
the probability of selecting at random a student who texts for more than 80 minutes.
the percentage of students who spend between 30 minutes and an hour texting.
the percentage of students who texted for fewer than 50 minutes.
the probability of selecting at random a student who texts for fewer than 15 minutes.
the percentage of students who spend more than 55 minutes texting.
the probability of selecting at random (with replacement) two students who spent a below-average amount of time texting.
the probability of selecting at random (with replacement) two students who spent more than 75 minutes texting.
the probability of selecting at random a student who spends an extreme amount of time texting – either less than 10 minutes OR more than 110 minutes.
the probability of selecting at random a student who spends between 10 and 30 minutes texting.
the percentile rank of a student who spent 100 minutes texting.
the two numbers of minutes that define the middle 95% of students in the distribution.
How learned
Gender
Self-taught
Learned in school
Private instruction
TOTAL
Female
12
38
72
Male
58
TOTAL
31
62
37
130
Explanation / Answer
Solution:-
a) The probability that particular student completed her/his intended major is 0.70.
b) The probability that two different randomly selected students both completed their intended major is 0.49.
The probability that particular student completed her/his intended major is 0.70.
The probability that two different randomly selected students both completed their intended major = 0.7 × 0.7 = 0.49
c) The probability that two different randomly selected students completed a different major than the one they intended is 0.09.
The probability that particular student completed a different major than the one they intended = 0.30
The probability that two different randomly selected students completed a different major than the one they intended = 0.30 × 0.30 = 0.09
d) The probability that one randomly selected student completed his/her intended major and another randomly selected student did not is 0.21.
The probability that particular student completed a different major than the one they intended = 0.30
The probability that particular student completed her/his intended major is 0.70.
The probability that one randomly selected student completed his/her intended major and another randomly selected student did not = 0.30 × 0.70 = 0.21.
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