5.1
Jay is a salesman who has kept up with his computer sales over the last year. Let X = the number of computers sold
in a day.
What is the probability that Jay will sell 3 computers in a given day?
P(3) = 0.2
The volumes of soda in quart soda bottles can be described by a Normal model with a mean of 32.3 oz
and a standard deviation of 1.2 oz.
What volume will represent the 20th percentile (the cut-off for the lower 20%)?
invNorm (0.2, 32.3, 1.2) = 31.29 ounces
Scores on the SAT verbal test in a recent year were approximately Normal with N(504, 111).
What is the proportion of students who scored between 450 and 550?
Normalcdf (450, 550, 504, 111) = 0.3474
Assume that 20% of college students wear contact lenses. We take a random sample of 300 college students.
What is the probability that more than 18% wear contact lenses?
Normalcdf(.18, infinity, .2,β.π(πβ.π)
πππ ) = 0.8068
irth weights at a local hospital have a Normal distribution with a mean of 110 oz and a standard deviation
of 15 oz.
What is the probability that the mean weight of a baby born at this hospital will be greater than
115 in a sample of 20 babies?
Normalcdf(115, infinity, 110, 15/sqrt(20)) = 0.0680
Jay is a salesman who has kept up with his computer sales over the last year. Let X = the number of computers sold in a day. What is the probability that Jay will sell at least 1 computer on a given day
0.8
The volumes of soda in quart soda bottles can be described by a Normal model with a mean of 32.3 oz
and a standard deviation of 1.2 oz.
In a sample of size 100, what is the probability that the mean volume is between 32.2 oz. and
32.4 oz?
normalcdf( 32.3, 32.4, 32.3, 1.2/sqrt(100)) 0.5953
Scores on the SAT verbal test in a recent year were approximately Normal with N(504, 111).
In a sample of 75 students, what is the probability that the mean verbal score will be below 490?
Normalcdf (-infinity, 490, 504, 111/sqrt(75)) = 0.1374
DAILY DOUBLE
Find the cut-off values that define the following regions for the standard Normal distribution
The middle 30%
invNorm (.35, 0 , 1) = -0.39 and invNorm (.65, 0, 1) = 0.39
irth weights at a local hospital have a Normal distribution with a mean of 110 oz and a standard deviation
of 15 oz.
What is the probability that a baby born at this hospital will have a weight greater than 125?
Normalcdf(125, infinity, 110,15) = 0.1587
If we roll a single die 4 times and record the number of sixes observed, we could generate a probability distribution, in which x is the number of sixes when rolling a die four times. What is the mean of the probability distribution?.
0.67
he volumes of soda in quart soda bottles can be described by a Normal model with a mean of 32.3 oz
and a standard deviation of 1.2 oz.
What is the probability that a randomly selected bottle will have a volume more than 34 oz?
normalcdf( 34, infinity, 32.3, 1.2) = 0.0783
Scores on the SAT verbal test in a recent year was approximately Normal with N(504, 111)
In a sample of 30 students, what is the probability that the mean verbal score will be between
490 and 500?
Normalcdf (490, 500, 504, 111/sqrt(30)) = 0.1769
Assume that 20% of college students wear contact lenses. We take a random sample of 300 college students.
What is the probability that fewer than 15% of the sample wear contact lenses?
Normalcdf(-infinity, .15, .2,β.π(πβ.π)
πππ ) = 0.0152
irth weights at a local hospital have a Normal distribution with a mean of 110 oz and a standard deviation
of 15 oz.
What is the probability that a baby born at this hospital will have a weight between 115 and 120?
Normalcdf(115 ,120, 110, 15) = 0.1169
If we roll a single die 4 times and record the number of sixes observed, we could generate a probability distribution, in which x is the number of sixes when rolling a die four times.
What is the probability of getting no more than 2 sixes in the four rolls?
P(X β€ 2) = 0.9838
he volumes of soda in quart soda bottles can be described by a Normal model with a mean of 32.3 oz
and a standard deviation of 1.2 oz.
In a sample of size 50, what is the probability that the mean volume is less than 32 oz?
normalcdf( - infinity, 32, 32.3, 1.2/sqrt(50)) = 0.0385
Scores on the SAT verbal test in a recent year was approximately Normal with N(504, 111).
What is the proportion of students who scored below 400?
Normalcdf(-infinity, 400, 504, 111) = 0.1744
Find the cut-off values that define the following regions for the standard Normal distribution
The top 10%
InvNorm (.9, 0,1) = 1.28
irth weights at a local hospital have a Normal distribution with a mean of 110 oz and a standard deviation
of 15 oz.
What mean weights would be the cut-off values defining the middle 10% for a sample of size 100?
invNorm(0.45, 110,15/sqrt(100)) = 109.81 and invNorm(0.55, 110,15/sqrt(100)) = 110.89
If we roll a single die 4 times and record the number of sixes observed, we could generate a probability distribution,
in which x is the number of sixes when rolling a die four times.
What is the probability of getting at least 2 sixes in the four rolls?
P(X β₯ 2) = 0.1319
The volumes of soda in quart soda bottles can be described by a Normal model with a mean of 32.3 oz
and a standard deviation of 1.2 oz.
a. What is the probability that a randomly selected bottle will have a volume less than 32 oz?
normalcdf( - infinity, 32, 32.3, 1.2) = 0.4013
Scores on the SAT verbal test in a recent year were approximately Normal with N(504, 111). How high must a student score to be in the top 10%?
invNorm ( .9, 504,111) = 646.25
Find the cut-off values that define the following regions for the standard Normal distribution
The bottom 30%
invNorm (.30, 0,1) = -0.52
irth weights at a local hospital have a Normal distribution with a mean of 110 oz and a standard deviation
of 15 oz.
What is the probability that a baby born at this hospital will have a weight less than 105?
Normalcdf(-infinity,105, 110, 15) = 0.3694