In 2011, the world's largest pumpkin weighed 825 kilograms. An average-sized pumpkin weighs 5,000 grams. The 2011 world-record p

The 99% confidence interval for the actual mean difference between average mail-order and internet purchase amounts falls within [$(-31.82), $12.02].

Step-by-step clarification:

We know a random sample of 16 mail-order sales receipts shows a mean sale amount of $74.50 and a standard deviation of $17.25.

For internet sales, a random sample of 9 receipts gives a mean sale amount of $84.40 with a standard deviation of $21.25.

The pivotal value utilized for constructing a 99% confidence interval for the true mean difference is given by;

                      P.Q.  =  

 ~

where,

= sample mean of mail-order sales = $74.50

= sample mean of internet sales = $84.40

= standard deviation for mail-order sales = $17.25

= standard deviation for internet sales = $21.25

= number of mail-order sales receipts = 16

= number of internet sales receipts = 9

Furthermore,  

 =   = 18.74

The actual mean difference between average mail-order and internet purchases is denoted by (

).

Thus, the 99% confidence interval for () is expressed as;

      = Here, the t critical value at the 0.5% significance level with 23 degrees of freedom is 2.807.           =

          = [$-31.82, $12.02]

Therefore, the 99% confidence interval for the true mean difference between average mail-order and internet purchases is [$(-31.82), $12.02].

Is there meant to be an image?

Answer:

When x = 72, the z score is:

The average is 58

This z-score indicates that x= 72 is 1.273 standard deviations above the mean.

Step-by-step explanation:

Let’s consider the following details for this question: John's typing speed on a test is assumed to follow a normal distribution. Let X denote the number of words he can type in a minute. Hence, X ~ N(58, 11). It’s important to round the result to three decimal points if needed.

Provide your response below for words per minute on a typing test conducted on Sunday. The z score when x = 72 is

In this scenario, we acknowledge that the variable under consideration is represented by a normal distribution:

The formula for the z score is as follows:

By substituting values, we derive:

The mean is 58

This z-score indicates that x= 72 is 1.273 standard deviations higher than the mean.

Let the three consecutive even integers representing the sides of triangle PQR be defined as x, (x + 2), and (x + 4). Given that the perimeter of triangle PQR equals 42 cm.

Step-by-step explanation:

The difference quotient represents the slope of the line connecting two points on a curve. To achieve the most accurate estimate, we need to use points that are nearest to x = 0. For this problem, the relevant points are (-0.001, 1.999) and (0.001, 2.001).

m = (2.001 − 1.999) / (0.001 − (-0.001))

m = 1