Ohlone College What Is the Probability of The Following Z Scores Questions

21) (4 pts) Fifty Part-time students were asked how many courses they were taking this term. The
(incomplete) results are shown below:
# of Courses
Frequency
Relative Frequency
1
2
3
30
15
0.6
Cumulative Relative
Frequency
a) Fill in the missing data
b) What percent of students take exactly two courses?
c) What percent of students take one or two courses?
22) (2 pts) What is the probability of the following Z-Scores
a)
Z ≤ 1.67
b) Z ≥ -2.68
23) (2 pts) Listed are 19 ages for students in a psychology class. The ages are listed in order from
smallest to largest.
18; 21; 22; 25; 26; 27; 29; 30; 31; 33; 36; 37, 41; 42; 47; 52; 55; 57; 58
a) Find the 40th percentile.
b) Find the 55th percentile
24) (4 pts) Suppose you have 12 cards. Seven of the cards are red and five of them are blue. The red
cards are numbered 1, 2, 3, 4, 5, 6, 7. The four blue cards are numbered 1, 2, 3, 4, 5. The cards
are well shuffled. You randomly draw one card.
Let A = Card drawn is red
Let B = Card drawn is odd-numbered
a. List the sample space
b.
c.
d.
e.
f.
P(A) = _____
P(A|B) = _____
P(A AND B) = _____
P(A OR B) = _____
Are A and B mutually exclusive? Justify your answer numerically. For example, show that they
either equal or do not equal with equations
25) (5 pts) Below are some random numbers that your professor thought up but cannot think of an
example to apply them to. Please use these numbers to answer the following questions.
3, 4, 5, 7, 9, 10, 11, 13
a.
b.
c.
d.
First quartile = _______
Second Quartile = _______
Third Quartile = _______
Interquartile Range (IQR) = _______
26) (5 pts) Find The mean median and mode of the following data. Then find the standard deviation.
Please show all of your work.
10, 7, 6, 10, 6, 15
Mean: _______
Median: _______
Mode: _______
Standard Deviation: _______
27) (2 pts) The average score on a class statistics exam is 75 with a standard deviation of 5. Find the
Z-Scores of the following scores and describe what the scores mean.
a) x = 72
b) x = 92
28) (2 pts) Using the information provided above (in question 27), find the x value given the Z score
a) Z = 1.5
b) Z = -2
29) (4 pts) A hospital researcher is interested in the number of times the average patient will ring
the nurse during a 12-hour shift. For a random sample of 20 patients, the following information
was obtained.
x
1
2
3
4
5
P(x)
0.15
0.05
x*P(x)
(x – μ)2P(x)
0.35
0.20
a) Define the random variable X.
b) Define P(x), or the probability of x.
c) Find the probability that a patient will ring the bell three times during a 12-hour shift.
P(x = 3) = _______
d) Find the probability that a patient will ring the bell at most four times
P(x ≤ 4) = _______
e) On average, how many times will a patient ring for a nurse during a 12-hour shift?
f)
Find the standard Deviation
Psych / Soc 15 Formulas
Exam 1
𝒇
𝑹𝑭 =
∑𝒙
𝝁=
𝝈=
𝝁 = 𝒙 ∗ 𝑷(𝒙)
𝑵
𝑴=
𝒔=
P(A OR B) = P(A) + P(B) – P(A AND B)
𝒏
∑𝒙
𝝈 = √(𝒙 − 𝝁)𝟐 ⋅ 𝑷(𝒙)
𝒏
̅)𝟐
∑(𝒙−𝒙
p+q=1
𝒏−𝟏
∑(𝒙−𝝁)𝟐
𝝈 = 𝒏𝒑𝒒
𝒏
𝟏 𝟏
𝝈 = √ ( − 𝟏)
IQR = Q3 – Q1
Median if Even =
i =
𝒌
(n+1)
𝟏𝟎𝟎
𝒙+𝟎.𝟓𝒚
𝒏
(100)
P(A|B) =
P(A AND B)
P(B)
𝒑 𝒑
𝑻𝒘𝒐 𝑴𝒊𝒅𝒅𝒍𝒆 𝑵𝒖𝒎𝒃𝒆𝒓𝒔
𝟐
Z=
𝒙−𝝁
𝝈
x = Z(𝝈) + 𝝁