The mean of the data set is 40 and one standard deviation is 5. About what percent of the numbers fall between 35 and 50?
1 answer:
Answer:
The correct option is D. 81.8%
Step-by-step explanation:
Mean of the data set is given to be 40
⇒ μ = 40
Standard deviation of the data set is given to be 5
⇒ σ = 5
Now we are supposed to find out what percent of the numbers fall between 35 and 50
Now for P(35 < x < 50) :
Substitute x = 35 ⇒ z = -1
Substitute x = 50 ⇒ z = 2
So, P(-1 < z < 2) = P(z < 2) - P(z < -1)
⇒ P(-1 < z < 2) = 0.9772 - 0.1587
⇒ P(-1 < z < 2) = 0.8185
⇒ P(-1 < z < 2) = 81.8%
Therefore, 81.8% percent of the numbers fall between 35 and 50
Hence, The correct option is D. 81.8%
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Answer:
So on this case the 80% confidence interval would be given by (3.003;3.297)
And the margin of error is given by:
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
population mean (variable of interest)
represent the population standard deviation
n=11 represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
(1)
Since the Confidence is 0.80 or 80%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NOR.INV(0.1,0,1)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 80% confidence interval would be given by (3.003;3.297)
And the margin of error is given by: