Question

Q3. The weights of pennies minted after 1982 are approximately normally distributed with mean 2.46 grams and standard deviation 0.02 grams. (a) Draw a normal curve with the parameters labeled and shade the region under the normal curve between 2.44 and 2.49 grams. (b) What is the value of the shaded region in the part (a) above? Provide two interpretations for this area.

Answer #1

Given mean and standard deviation

Let and

and

a)

The weights of pennies minted after 1982 are Normally
distributed with mean 2.46 grams and standard deviation .02
grams.
For a penny to be among the heaviest 10% of all pennies, what
must it weigh? (A sketch is often helpful for this type of
problem)
Supposeasampleof10penniesisrandomlyselectedfromthepopulationof
pennies. What is the probability that the average of this sample is
more than 2.47 grams?
Now, instead, if a sample of 30 pennies is randomly selected
from the population, what is the probability...

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randomly selected pennies minted after 1982. 2.46 2.47 2.49 2.48
2.50 2.44 2.46 2.45 2.49 2.47 2.45 2.46 2.45 2.46 2.47 2.44
2.45
a) Use an unbiased estimator to compute the point estimate of
the population mean weight of pennies minted after 1982.
b) Use an unbiased estimator to compute the point estimator of
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0.0048 ). Do not write as a percentage .
The weights of broilers (commercially raised chickens) are
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Assume the random variable X is normally distributed with
mean
mu equals 50
and standard deviation
sigma equals 7
.
Compute the probability. Be sure to draw a normal curve with the
area corresponding to the probability shaded.
Upper P left parenthesis Upper X greater than 39 right
parenthesis
LOADING...
Click the icon to view a table of areas under the normal
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Which of the following normal curves corresponds to
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1. The weights of a certain dog breed are approximately normally
distributed with a mean of ? = 46 pounds, and a standard deviation
of ? = 7 pounds.
A) A dog of this breed weighs 51 pounds. What is the dog's
z-score? Round your answer to the nearest hundredth as needed. z
=
B) A dog has a z-score of -0.8. What is the dog's weight? Round
your answer to the nearest tenth as needed. ____ pounds
C) A...

1. The weights of bags of baby carrots are normally
distributed, with a mean of 29 ounces and a standard deviation of
0.31 ounce. Bags in the upper 4.5% are too heavy and must be
repackaged. What is the most a bag of baby carrots can weigh and
not need to be repackaged?
2. The area between z= -1.1 and z =0.7 under the standard normal
curve is
3.
Find the indicated area under the standard normal curve
To the...

Assume the random variable X is normally distributed with mean
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mean mu equals 53 and standard deviation sigma equals 11. Compute
the probability. Be sure to draw a normal curve with the area
corresponding to the probability shaded. Upper P left parenthesis
Upper X less than or equals 40 right parenthesis Which of the
following shaded regions corresponds to Upper P left parenthesis
Upper X less than or equals 40 right parenthesis? A. X 4053 A
normal curve has a...

Assume that the random variable X is normally distributed, with
mean mu equals 53 and standard deviation sigma equals 11. Compute
the probability. Be sure to draw a normal curve with the area
corresponding to the probability shaded. Upper P left parenthesis
Upper X less than or equals 40 right parenthesis Which of the
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