The percentage error is 23%
Explanation:
The estimated total cost of the groceries = $50
The actual cost of the groceries = $65
To find the error value, we need to subtract the value of actual cost and total cost of the groceries.
Thus,
error value = actual cost - total cost
error value
Hence, error value = $15
The formula to determine the percent error is given by
Substituting the values in the formula, we get,
Rounding off the value, we have, 23%
Thus, the percentage error is 23%
Answer:
The interval that describes how long it takes for passengers to board the middle 95% of the time is between 40.16 minutes and 55.84 minutes.
Step-by-step explanation:
Problems of normally distributed samples can be 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:
.
Which interval describes how long it takes for passengers to board the middle 95% of the time?
This is between the 2.5th percentile and the 97.5th percentile.
So this interval is the value of X when Z has a a pvalue of 0.025 and the value of X when Z has a pvalue of 0.975
Lower Limit
Z has a pvalue of 0.025 when . So
Upper Limit
Z has a pvalue of 0.975 when . So
The interval that describes how long it takes for passengers to board the middle 95% of the time is between 40.16 minutes and 55.84 minutes.