The answer is 0.81 repeating
To find the margin of error, multiply the z-score by the standard deviation, then divide by the square root of the sample size.The z*-score for a 90% confidence level is 1.645.The margin of error is 0.20.The confidence interval is 48.3 to 48.7.48.8 is not within the confidence interval.
Answer:
And using a calculator, excel or the normal standard table we have that:
Step-by-step explanation:
Previous concepts
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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the weigths of a population, and for this case we know the distribution for X is given by:
Where
and
Since the distribution for X is normal then we know that the distribution for the sample mean
is given by:
We can find the probability required with the following z score formula:

And replacing we got:
And using a calculator, excel or the normal standard table we have that:
I am not sure! What is the original equation?