Laurie needs at least 40 pounds of topsoil for a new flower bed. Each bag of topsoil is 200 ounces. Laurie determines that if sh
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This question is solved using the central limit theorem, giving an answer of:
Fourth option, approximately normal with mean of 140 seconds and standard deviation of 10 seconds.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 140, standard deviation of 20, sample of 4:
By the Central Limit Theorem, the distribution is approximately normal.
Mean is the same, of 140.
, thus:
Thus, the correct answer is:
Fourth option, approximately normal with mean of 140 seconds and standard deviation of 10 seconds.
For another example of the Central Limit Theorem, you can check brainly.com/question/15519207
Answer:
The 95% confidence interval would be given by (96.98;100.82)
Step-by-step explanation:
Information given
represent the sample mean
population mean (variable of interest)
s=0.62 represent the sample standard deviation
n=103 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
(1)
The degrees of freedom are given by:
Since the Confidence is 0.95 or 95%, the significance is and
, and the critical value for this case would be
And replacing we got:
The 95% confidence interval would be given by (96.98;100.82)