Answer:
a) The formula is given by mean
the margin of error. Where the margin of error is the product between the critical value from the normal standard distribution at the confidence level selected and the standard deviation for the sample mean.
b)
Step-by-step explanation:
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".
If the distribution for X is normal or if the sample size is large enough we know that the distribution for the sample mean
is given by:
Part a
The formula is given by mean
the margin of error. Where the margin of error is the product between the critical value from the normal standard distribution at the confidence level selected and the standard deviation for the sample mean.
Part b
The confidence interval for the mean is given by the following formula:
Answer:
x ≈ 34.88 square cm
Step-by-step explanation:
Solve by proportional formula:
Area of a sector/area of circle* = sector central arc measure/360
*area of a circle = πr²
x/(53.29π) = 75/360
x/53.29π = 0.2083
x = 11.1020833π
x = 34.8782233
x ≈ 34.88 square cm
The answer isnin the pictures
Next to angle x is 102° and is you add 102 to angle x it has to equal 180 because that’s the value of half the circle so you do 180-102 which will give you 78