Answer: Since the sample size is large (n > 30) and the population standard deviation is known, we can use the normal distribution to approximate the sampling distribution of the mean.
The standard error of the mean is the standard deviation of the sampling distribution of the mean, and it can be calculated as follows:
standard error of the mean = standard deviation / sqrt(n)
Plugging in the given values, we get:
standard error of the mean = 7 inches / sqrt(51) = 1.17 inches
The probability that x is within 0.5 inches of the claimed population mean (15 inches) is equal to the probability that x is between 14.5 inches and 15.5 inches. We can use the normal distribution to find this probability by standardizing the range 14.5 inches to 15.5 inches and using a z-table or a calculator to find the corresponding probability.
The standardized value for 14.5 inches is (14.5 - 15) / 1.17 = -0.43, and the standardized value for 15.5 inches is (15.5 - 15) / 1.17 = 0.43.
The probability that x is between -0.43 and 0.43 is equal to the area under the standard normal curve between these two values. Using a z-table or a calculator, we can find that this probability is 0.6915.
Therefore, the probability that x is within 0.5 inches of the claimed population mean is approximately 0.6915, which is the final answer.
Average Bloxyy
Which is not an equation of the line going through (3, -6) and (1, 2)?
A. y=-4x+6
B. y+ 6 = -4(x- 3)
C. y- 1=-4(x-2)
D. y - 2 = -4(x-1)
An equation of the line going through two points (x1, y1) and (x2, y2) can be written in the form y - y1 = m(x - x1), where m is the slope of the line. The slope of the line can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the values for (x1, y1) and (x2, y2) from the problem, we get:
m = (2 - (-6)) / (1 - 3) = 8/ -2 = -4
Therefore, an equation of the line going through (3, -6) and (1, 2) is of the form y - (-6) = -4(x - 3).
Option B is of this form, so it is an equation of the line going through (3, -6) and (1, 2). The other options are not of this form, so they are not equations of the line going through (3, -6) and