Exercise 2.66. You are given a fair die. You must decide ahead of time how many times to roll. If you get exactly 2 sixes, you g
1 answer:
Answer:
The number of rolls = 36
Step-by-step explanation:
Thinking process:
A die has six sides (6).
Thus, the probability of striking a 6 is
Let the number or sixes be 2
The number of roles for the die is given the following: where n is the number of sixes needed.
Therefore, the number of roles needed =
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Answer:
The 95% confidence interval would be given by (5.139;5.861)
Step-by-step explanation:
1) Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean for the sample
population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
2) Confidence interval
Assuming that and the ranfom sample n=1086.
The confidence interval for the mean is given by the following formula:
(1)
In order to calculate the critical value we need to find first the degrees of freedom, given by:
Since the Confidence is 0.98 or 98%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.01,1085)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by (5.139;5.861) We are 98% confident that the mean time spent volunteering for the population of parents of school-aged children is between these two values.
Answer: The required scale factor of the dilation is 4.
Step-by-step explanation: Given that the parallelogram FGHJ was dilated and translated to form similar parallelogram F'G'H'J'.
We are to find the scale factor of the dilation.
From the graph, we note that
JH = 2 units and J'H' = 8 units.
We know that
Therefore, the scale factor of the given dilation is
Thus, the required scale factor of the dilation is 4.
Answer:
0.4 ft
Step-by-step explanation:
It can be convenient to let a spreadsheet compute the values for you. Here, we have written an explicit formula for the height of the n-th bounce:
h = 5.5×0.64^(n-1)
We have written the formula this way because we are given the height of the first bounce, not the starting height. Each bounce multiplies the height by a factor of 0.64. Then the 7th bounce will have a height of ...
h = 5.5×0.64^6 ≈ 0.378 ≈ 0.4 . . . . feet
