Which of the following is(are) True? I. The means of the Student’s t and standard normal distributions are equal. II. The standard normal distribution approaches the Student’s t distribution as the degrees of freedom becomes large. A. I only B. II only C. Both I and II D. Neither I nor II

Describe in words the surface whose equation is given. (assume that r is not negative.) $\theta =\frac{\pi }{4}$
a) The plane $y=-z$ where y is not negative
b) The plane $y=z$ where y and z are not negative
c) The plane $y=x$ where x and y are not negative
d) The plane $y=-x$ where y is not negative
e) The plane $x=z$ where x and y are not negative

Explain why t distributions tend to be flatter and more spread out than the normal distribution.

The manager of the store in the preceding exercise calculated the residual for each point in the scatterplot and made a dotplot of the residuals.
The distribution of residuals is roughly Normal with a mean of $0 and standard deviation of $22.92.
The middle 95% of residuals should be between which two values? Use this information to give an interval of plausible values for the weekly sales revenue if 5 linear feet are allocated to the stores

An important factor in solid missile fuel is the particle size distribution. Significant problems occur if the particle sizes are too large. From production data in the past, it has been determined that the particle size (in micrometers) distribution is characterized by ${\displaystyle f\left(x\right)=3x^{-4},f\text{or}x>1,f\left(x\right)=0}$, elsewhere.
a) Verify that this is a valid density function.
b) Evalute F(x).
c) What is the probability that a random particle from the manufactured fuel exceeds 4 micrometers?

Use the Sample Variance Definition to find the variance and standard deviation of the data. Round the answers to one decimal place.
8, 7, 3, 2, 10, 4

A yoga class consists of 90 males and 110 females. What is the ratio of male to female students?

LightCastle Partners, a Bangladeshi business management consultant, employs a large number of data analysts to analyze the data in a survey project. The time it takes for new data analysts to learn the analysts procedure is known to have a normal distribution with a mean of 82 minutes and a standard deviation of 11 minutes.
a. What is the probability that the new data analysts will take more than 77 minutes to learn the analysis procedure?
b. What is the probability that the new data analysts will take between 54 to 85 minutes to learn the analysis procedure?
c. To maintain employee standars, LightCastle does not hire any analyst who fails to learn the process within a specified time. Therefore, what should be the specified time limit if they wish to retain at most 72.67% of new analysts?
? minutes