ALTA EXAM PRACTICE QUESTIONS AND
CORRECT ANSWERS!!
Stephanie gets an average of 11 calls during her 8 hour work day. What is the probability
that Stephanie will get more than 4 calls in a 2 hour portion of her work day? (Round your
answer to three decimal places.)
$0.144$0.144
The time interval of interest is 2 hours. There is an average of 11 calls per 8 hours or 1182=114
calls per 2 hours. The probability can be found using the Poisson distribution with parameter
λ=114. Let X be the number of calls that are received in the 2 hour time period. According to the
formula, we find:
P(X=x)=λxe−λx!
Since it is easier to find X equal to or less than 4, we use the
compliment:P(X>4)=1−(P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4))P(X>4)=1−((114)0e−1140!
+(114)1e−1141!+(114)2e−1142!+(114)3e−1143!+(114)4e−1144!)1−(0.064+0.176+0.242+0.222
+0.152)≈0.144
On average, Mary has noticed that 18 trains pass by her house daily (24 hours) on the
nearby train tracks. What is the probability that exactly 1 train will pass her house in a 3
hour time period?
Round the final answer to three decimal places.
$0.237$0.237
The time interval of interest is 3 hours. There is an average of 18 trains per 24 hours or
18243=94 trains per 3 hours. The probability can be found using the Poisson distribution with
parameter λ=94. Let X be the number of trains that pass in the 3 hour time period. According to
the formula, we find:
P(X=x)=λxe−λx!
P(X=1)=(94)1e−941!
≈0.237
,According to a 2011 Pew Research poll, cell owners make or receive an average of 12 phone
calls each day.
Let X = the number of phone calls that smartphone users send or receive per day. The
random variable X has a Poisson distribution: X ~ P(12).
What is the probability that a smartphone user makes or receives exactly 20 phone calls in
2 days? (Round to the thousandths place.)
0.062
To find the probability of a Poisson Distribution, use the formula:
f(x)=e−μ⋅μxx!
...where μ is the average, and x is the number of successes the question is asking about. In this
question, the value of x is 20 because that is the number of phone calls (or successes) that the
question is asking about.
However, the interval is changed from 1 day to 2 days, so μ should be doubled. The average
number of phone calls per day is 12, and 12⋅2=24. So the new value of μ is 24.
Plugging these values into the equation, you get:
f(x)=e−24⋅242020!
...which simplifies to 0.062, rounded to the thousandths digit.
According to a recent poll, smart phone users receive an average of 4 phone calls each day.
Let X = the number of phone calls that smartphone users receive per day. The random
variable X has a Poisson distribution: X ~ P(4).
What is the probability that a smartphone user receives at most 2 phone calls per day?
(Round to the thousandths place.)
0.238
To find the probability of a Poisson Distribution, use the formula:
f(x)=e−μ⋅μxx!
...where μ is the average, and x is the number of successes the question is asking about.
In this question, μ is 4, the average number of phone calls smartphone users receive in a day. The
, value of x is 2 because that is the number of phone calls (or successes) that the question is asking
about. But since the question asks for "at most 2," you must find the probility of
P(X=0)+P(X=1)+P(X=2), all of the possible values of 2 or less.
Plugging these values into the equation, you get:
f(x)f(x)=P(X=0)+P(X=1)+P(X=2)=e−4⋅400!+e−4⋅411!+e−4⋅422!≈0.018316+0.073263+0.14652
5
...which simplifies to 0.238, rounded to the thousandths digit.
According to a recent poll, smart phone users receive an average of 4 phone calls each day.
Let X = the number of phone calls that smartphone users receive per day. The random
variable X has a Poisson distribution: X ~ P(4).
What is the probability that a smartphone users receives exactly 3 phone calls per day?
(Rounded to the thousandths place.)
0.195
To find the probability of a Poisson Distribution, use the formula:
f(x)=e−μ⋅μxx!
...where μ is the average, and x is the number of successes the question is asking about. In this
question, μ is 4, the average number of phone calls smartphone users receive in a day. The value
of x is 3 because that is the number of phone calls (or successes) that the question is asking
about.
Plugging these values into the equation, you get:
f(x)=e−4⋅433!
...which simplifies to 0.195, rounded to the thousandths digit.
Michelle gets an average of 19 calls during her 8 hour work day. What is the probability
that Michelle will get exactly 6 calls in a 2 hour portion of her work day?
Round your answer to three decimal places.
$0.138$0.138
The time interval of interest is 2 hours. There is an average of 19 calls per 8 hours or 1982=194
CORRECT ANSWERS!!
Stephanie gets an average of 11 calls during her 8 hour work day. What is the probability
that Stephanie will get more than 4 calls in a 2 hour portion of her work day? (Round your
answer to three decimal places.)
$0.144$0.144
The time interval of interest is 2 hours. There is an average of 11 calls per 8 hours or 1182=114
calls per 2 hours. The probability can be found using the Poisson distribution with parameter
λ=114. Let X be the number of calls that are received in the 2 hour time period. According to the
formula, we find:
P(X=x)=λxe−λx!
Since it is easier to find X equal to or less than 4, we use the
compliment:P(X>4)=1−(P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4))P(X>4)=1−((114)0e−1140!
+(114)1e−1141!+(114)2e−1142!+(114)3e−1143!+(114)4e−1144!)1−(0.064+0.176+0.242+0.222
+0.152)≈0.144
On average, Mary has noticed that 18 trains pass by her house daily (24 hours) on the
nearby train tracks. What is the probability that exactly 1 train will pass her house in a 3
hour time period?
Round the final answer to three decimal places.
$0.237$0.237
The time interval of interest is 3 hours. There is an average of 18 trains per 24 hours or
18243=94 trains per 3 hours. The probability can be found using the Poisson distribution with
parameter λ=94. Let X be the number of trains that pass in the 3 hour time period. According to
the formula, we find:
P(X=x)=λxe−λx!
P(X=1)=(94)1e−941!
≈0.237
,According to a 2011 Pew Research poll, cell owners make or receive an average of 12 phone
calls each day.
Let X = the number of phone calls that smartphone users send or receive per day. The
random variable X has a Poisson distribution: X ~ P(12).
What is the probability that a smartphone user makes or receives exactly 20 phone calls in
2 days? (Round to the thousandths place.)
0.062
To find the probability of a Poisson Distribution, use the formula:
f(x)=e−μ⋅μxx!
...where μ is the average, and x is the number of successes the question is asking about. In this
question, the value of x is 20 because that is the number of phone calls (or successes) that the
question is asking about.
However, the interval is changed from 1 day to 2 days, so μ should be doubled. The average
number of phone calls per day is 12, and 12⋅2=24. So the new value of μ is 24.
Plugging these values into the equation, you get:
f(x)=e−24⋅242020!
...which simplifies to 0.062, rounded to the thousandths digit.
According to a recent poll, smart phone users receive an average of 4 phone calls each day.
Let X = the number of phone calls that smartphone users receive per day. The random
variable X has a Poisson distribution: X ~ P(4).
What is the probability that a smartphone user receives at most 2 phone calls per day?
(Round to the thousandths place.)
0.238
To find the probability of a Poisson Distribution, use the formula:
f(x)=e−μ⋅μxx!
...where μ is the average, and x is the number of successes the question is asking about.
In this question, μ is 4, the average number of phone calls smartphone users receive in a day. The
, value of x is 2 because that is the number of phone calls (or successes) that the question is asking
about. But since the question asks for "at most 2," you must find the probility of
P(X=0)+P(X=1)+P(X=2), all of the possible values of 2 or less.
Plugging these values into the equation, you get:
f(x)f(x)=P(X=0)+P(X=1)+P(X=2)=e−4⋅400!+e−4⋅411!+e−4⋅422!≈0.018316+0.073263+0.14652
5
...which simplifies to 0.238, rounded to the thousandths digit.
According to a recent poll, smart phone users receive an average of 4 phone calls each day.
Let X = the number of phone calls that smartphone users receive per day. The random
variable X has a Poisson distribution: X ~ P(4).
What is the probability that a smartphone users receives exactly 3 phone calls per day?
(Rounded to the thousandths place.)
0.195
To find the probability of a Poisson Distribution, use the formula:
f(x)=e−μ⋅μxx!
...where μ is the average, and x is the number of successes the question is asking about. In this
question, μ is 4, the average number of phone calls smartphone users receive in a day. The value
of x is 3 because that is the number of phone calls (or successes) that the question is asking
about.
Plugging these values into the equation, you get:
f(x)=e−4⋅433!
...which simplifies to 0.195, rounded to the thousandths digit.
Michelle gets an average of 19 calls during her 8 hour work day. What is the probability
that Michelle will get exactly 6 calls in a 2 hour portion of her work day?
Round your answer to three decimal places.
$0.138$0.138
The time interval of interest is 2 hours. There is an average of 19 calls per 8 hours or 1982=194
