Trapezoid L'M'N'P' was constructed using trapezoid LMNP. On a coordinate plane, 2 trapezoids are shown. Line segments connect ea

Response:

a) The average is 10 and the variance is 0.0625.

b) 0.6826 = 68.26% likelihood that the average time of visitors falls within 15 seconds of 10 minutes.

c) 10.58 minutes.

Step-by-step clarification:

To figure this out, we must comprehend the normal probability distribution alongside the central limit theorem.

Normal Probability Distribution

Issues involving normal distributions can be resolved using the z-score formula.

For a data set with mean and standard deviation , the z-score related to a measure X is defined as:

The z-score illustrates how many standard deviations the measure is positioned from the mean. Once the z-score is calculated, we refer to the z-score table to find the p-value matching this z-score. This p-value reflects the likelihood that the measurement is less than X, which means it indicates the percentile of X. To determine the chance that the measure exceeds X, we subtract the p-value from 1.

Central Limit Theorem

The Central Limit Theorem states that for a normally distributed random variable X, defined by mean and standard deviation , the sampling distribution of sample means of size n can be approximated as a normal distribution with mean and standard deviation .

For non-normal distributions, this theorem applies if n is at least 30.

In this case, the distribution has a mean of 10 minutes and a standard deviation of 2 minutes.

This indicates that

Assuming 64 visitors independently access the site.

This implies that

a. The expected value and variance of the average time of the visitors.

b. The chance that the mean visit duration is within 15 seconds of 10 minutes.

15 seconds = 15/60 = 0.25 minutes, thus between 9.75 and 10.25 seconds, which corresponds to the p-value of z when X = 10.25 minus the p-value of z when X = 9.75.

X = 10.25

Through the Central Limit Theorem

has a p-value of 0.8413.

X = 9.75

has a p-value of 0.1587.

0.6826 = 68.26% chance that the average visitor time is within 15 seconds of 10 minutes.

This corresponds to the 99th percentile, denoting X when Z equals a p-value of 0.99, hence X when Z = 2.327.

Thus, the result is 10.58 minutes.

Answer:

A list detailing the correct and incorrect prices is unavailable, making it impossible to ascertain precise answers.

Step-by-step explanation:

N.B: Without a provided list, accurate pricing cannot be guaranteed.

Manually entering barcodes or prices in an effort to determine costs can introduce mistakes in the selling price. This could adversely affect the business due to possible underpricing or overpricing.

For instance, a dress was priced at $30 incorrectly when it should have been $39. Conversely, the price of a t-shirt was accurately documented at $10. Meanwhile, the jeans were listed at $25 instead of the correct price of $23. This example illustrates two pricing errors involving clothing items: the dress is priced too low, while the jeans are priced too high.