Gabriel has a stack of nickels that is 0.72 inch tall. The thickness of a nickel is 0.08 inch. How many nickels does Gabriel hav
1 answer:
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You need to make 23 sales
Answer:
Choice C: approximately 121 green beans will be 13 centimeters or shorter.
Step-by-step explanation:
What's the probability that a green bean from this sale is shorter than 13 centimeters?
Let the length of a green bean be centimeters.
follows a normal distribution with
- mean
and
- standard deviation
.
In other words,
,
and the probability in question is .
Z-score table approach:
Find the z-score of this measurement:
. Closest to 0.86.
Look up the z-score in a table. Keep in mind that entries on a typical z-score table gives the probability of the left tail, which is the chance that will be less than or equal to the z-score in question. (In case the question is asking for the probability that
is greater than the z-score, subtract the value from table from 1.)
.
"Technology" Approach
Depending on the manufacturer, the steps generally include:
- Locate the cumulative probability function (cdf) for normal distributions.
- Enter the lower and upper bound. The lower bound shall be a very negative number such as
. For the upper bound, enter
- Enter the mean and standard deviation (or variance if required).
- Evaluate.
For example, on a Texas Instruments TI-84, evaluating gives
.
As a result,
.
Number of green beans that are shorter than 13 centimeters:
Assume that the length of green beans for sale are independent of each other. The probability that each green bean is shorter than 13 centimeters is constant. As a result, the number of green beans out of 150 that are shorter than 13 centimeters follow a binomial distribution.
- Number of trials
: 150.
- Probability of success
: 0.804317.
Let be the number of green beans out of this 150 that are shorter than 13 centimeters.
.
The expected value of a binomial random variable is the product of the number of trials and the probability of success on each trial. In other words,
The expected number of green beans out of this 150 that are shorter than 13 centimeters will thus be approximately 121.
Answer:
4 2/7
Step-by-step explanation:
It is convenient to let a spreadsheet or graphing calculator do the tedious math for you. (See the attachment.)
_____
The sum of the numbers is 56, so their average is 56/7 = 8. Then the absolute deviations from average are ...
... 8, 5, 2, 1, 3, 5, 6
and the total of these is 30. The mean absolute deviation is this sum divided by the number of numbers, 7, so is ...
... 30/7 = 4 2/7
_____
<em>More about Absolute Deviation from Average</em>
"Absolute" here refers to the absolute value function, which drops the sign of a negative number. The absolute deviation of the data value 0 is ...
... |0 - 8| = |-8| = 8
For 3, it is ...
... |3 - 8| = |-5| = 5
