The price of an item yesterday was $120. Today, the price fell to $78
2 answers:
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Answer:
So the answer for this case would be n=1337 rounded up to the nearest integer
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".
represent the sample mean for the sample
population mean (variable of interest)
represent the population standard deviation
n represent the sample size
Solution to the problem
The margin of error is given by this formula:
(a)
And on this case we have that ME =0.07 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
The critical value for 98% of confidence interval now can be founded using the normal distribution. And in excel we can use this formula to find it:"=-NORM.INV(0.01;0;1)", and we got , replacing into formula (b) we got:
So the answer for this case would be n=1337 rounded up to the nearest integer
Answer:
99.89% of students scored below 95 points.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
What percent of students scored below 95 points?
This is the pvalue of Z when X = 95. So
has a pvalue of 0.9989.
99.89% of students scored below 95 points.