Answer:
( $74.623, $83.777)
The 90% confidence interval is = ( $74.623, $83.777)
Critical value at 90% confidence = 1.645
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = $79.20
Standard deviation r = $10.41
Number of samples n = 14
Confidence interval = 90%
Using the z table;
The critical value that should be used in constructing the confidence interval.
z(α=0.05) = 1.645
Critical value at 90% confidence z = 1.645
Substituting the values we have;
$79.20+/-1.645($10.42/√14)
$79.20+/-1.645($2.782189528308)
$79.20+/-$4.576701774067
$79.20+/-$4.577
( $74.623, $83.777)
The 90% confidence interval is = ( $74.623, $83.777)
Answer:
Let X the random variable that represent the heights 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 the we know that the distribution for the sample mean
is given by:
And the standard error is given by:

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 heights 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 the we know that the distribution for the sample mean
is given by:
And the standard error is given by:

Ben is taller
Ben: 5 5/16 feet = 1.61925 meters
Marcus: 5 7/24 feet = 1.6129 meters
Answer:
Step-by-step explanation:
×7 = 
Answer:
N=12
Step-by-step explanation: