Timothy makes reduced copies of a photograph that has an actual length of 8 in. Each time he presses the reduce button on the co
1 answer:
Answer:
length of the photograph will be 4.2 in. after pressing the button 5 times.
Step-by-step explanation:
By pressing the button, every time size of the photograph gets reduced by 12%.
Therefore, the sequence formed by the reduced sizes of the photo will be a geometric sequence and the formula for the size of the reduced image will be,
L =
Where l = Actual length of the photograph
L = length of the reduced image
n = Number of times the button has been pressed
For l = 8 in. and n = 5
L =
=
= 4.22 in
L ≈ 4.2 in.
Therefore, length of the photograph will be 4.2 in. after pressing the button 5 times.
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Answer:
The 98% confidence interval would be given by (0.326;0.354)
Step-by-step explanation:
1) Notation and definitions
number of people who live within 20 miles of the coast in high hurricane risk counties of eight southern states
random sample taken
estimated proportion of people who live within 20 miles of the coast in high hurricane risk counties of eight southern states
true population proportion of people who live within 20 miles of the coast in high hurricane risk counties of eight southern states
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".
The population proportion have the following distribution
2) Confidence interval
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 98% of confidence, our significance level would be given by and
. And the critical value would be given by:
The confidence interval for the mean is given by the following formula:
If we replace the values obtained we got:
The 98% confidence interval would be given by (0.326;0.354)