Identify which of the following is not a property of the standard normal curve.
answer
It has inflection points at
?±2?.
question
The standard normal probability distribution has a mean of? _______ and a standard deviation of? _______.
answer
zero, one
question
Determine whether the following graph can represent a normal density function. Can this graph represent a normal density function?
answer
yes
question
Determine whether the following graph can represent a normal density function.Could the graph represent a normal density? function?
answer
no
question
The relative frequency histogram represents the length of phone calls on? George's cell phone during the month of September. Determine whether or not the histogram indicates that a normal distribution could be used as a model for the variable.
answer
yes because the histogram has the shape of a normal curve
question
One graph in the figure represents a normal distribution with mean
?=16 and standard deviation
?=3. The other graph represents a normal distribution with mean ?=9
and standard deviation ?=3.
Determine which graph is which and explain how you know.
answer
Graph A has a mean of
mu?equals=9
and graph B has a mean of
mu?equals=16
because a larger mean shifts the graph to the right.
question
If the area under the standard normal curve between
zequals=minus?1.46
and
zequals=0
is? 0.4279, then what is the area under the standard normal curve between
zequals=0
and
zequals=?1.46?
answer
Due to the symmetry of the standard normal? curve, the area between zequals=0 and the given negative? z-value will be the same as the area between zequals=0 and the same positive? z-value.
0.4279
question
If the area to the left of a? z-score is less than? 0.5, what must be? true?
answer
The? z-score must be negative.
question
If the area to the left of a? z-score is greater than? 0.5, what must be? true?
answer
The? z-score must be positive.
question
Find the? Z-scores that separate the middle
41?% of the distribution from the area in the tails of the standard normal distribution.
answer
-.54, .54
1) 1-.41=.59
2).59/2=.295
3) -.295 z score=-.54
question
A study was conducted that resulted in the following relative frequency histogram. Determine whether or not the histogram indicates that a normal distribution could be used as a model for the variable.
answer
The histogram is not? bell-shaped, so a normal distribution could not be used as a model for the variable.
question
Find the area under the normal curve to the left of -3 and 3.
answer
1) 3=.99865
2)-3=.00135
3) 1-(.99865-.00135)
question
P(x>38) mean=50 stdv=7
answer
=(x-mean)/standard deviation
1)=-1.714
2)z score =.04363
3) 1-.04363=.9564
or stat crunch
question
Assume that the random variable X is normally? distributed, with mean
?=62 and standard deviation ?=10.
Compute the probability
?P(56
answer
stat crunch-stat-calc-normal
question
The mean incubation time of fertilized eggs is 22 days. Suppose the incubation times are approximately normally distributed with a standard deviation of 1 day.
?(a) Determine the 19th percentile for incubation times.
?(b) Determine the incubation times that make up the middle 39?%.
answer
a) stat crunch-stat-calc-normal
mean=22 stdv=1 and =.19
=21
b) look at stat crunch chart and put middle
question
Find the area of the shaded region. The graph to the right depicts IQ scores of? adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
answer
.7248 stat crunch, between values
question
Steel rods are manufactured with a mean length of
24 centimeter? (cm). Because of variability in the manufacturing? process, the lengths of the rods are approximately normally distributed with a standard deviation of
0.07cm.
a)What proportion of rods has a length less than
23.9cm?
b) Any rods that are shorter than 23.83
cm or longer than 24.17 cm are discarded. What proportion of rods will be? discarded?
c)Using the results of part? (b), if
5000 rods are manufactured in a? day, how many should the plant manager expect to? discard?
d)If an order comes in for 10,000 steel? rods, how many rods should the plant manager expect to manufacture if the order states that all rods must be between 23.9 cm and 24.1 ?cm?
answer
a) stat crunch-stat-calc-norm plug in #'s
b) Convert the values of X to? Z-scores using
Zequals=StartFraction Upper X minus mu Over sigma EndFractionX???.
Then use a standard normal table to find the appropriate area under the normal curve.
c)To determine the correct? answer, multiply the proportion of rods that will be discarded by the total number of rods that are manufactured.
d)First determine the proportion of rods that are between
23.923.9
cm and
24.124.1
cm by converting the values of X to? Z-scores using
Zequals=StartFraction Upper X minus mu Over sigma EndFractionX???.
Then use this proportion to find the expected number of rods that must be manufactured.
question
The 78th percentile is
answer
stat crunch plug in .78 in =
question
Assume that human body temperatures are normally distributed with a mean of 98.22°F and a standard deviation of 0.64°F.
a. A hospital uses 100.6°F as the lowest temperature considered to be a fever. What percentage of normal and healthy persons would be considered to have a? fever? Does this percentage suggest that a 100.6°F is? appropriate?
b. Physicians want to select a minimum temperature for requiring further medical tests. What should that temperature? be, if we want only? 5.0% of healthy people to exceed? it? (Such a result is a false? positive, meaning that the test result is? positive, but the subject is not really? sick.)
answer
a)plug in stat crunch and 100.6 for () and do 1-.99=.01%
?Yes, because there is a small probability that a normal and healthy person would be considered to have a fever.
b) 99.28
x-98.22/.64=95=1.64 on z chart
x-98.22/.64=1.64
x=(1.64)(.64)+98.22
x=99.27
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