A random sample is selected from a population with mean μ = 102 and standard deviation σ = 10. For which of the sample sizes would it be reasonable to think that the x sampling distribution is approximately normal in shape? (Select all that apply.) a. n = 14 b. n = 19 c. n = 45 d. n = 55 e. n = 110 f. n = 440

Since we can't assume that the distribution of X is the normal then we need to apply the central limit theorem in order to approximate the with a normal distribution. And we need to check if n>30 since we need a sample size large as possible to assume this.

Based on this rule we can conclude:

a. n = 14 b. n = 19 c. n = 45 d. n = 55 e. n = 110 f. n = 440

Only for c. n = 45 d. n = 55 e. n = 110 f. n = 440 we can ensure that we can apply the normal approximation for the sample mean

for n=14 or n =19 since the sample size is <30 we don't have enough evidence to conclude that the sample mean is normally distributed

Step-by-step explanation:

For this case we know that for a random variable X we have the following parameters given:

Since we can't assume that the distribution of X is the normal then we need to apply the central limit theorem in order to approximate the with a normal distribution. And we need to check if n>30 since we need a sample size large as possible to assume this.

Based on this rule we can conclude:

a. n = 14 b. n = 19 c. n = 45 d. n = 55 e. n = 110 f. n = 440

Only for c. n = 45 d. n = 55 e. n = 110 f. n = 440 we can ensure that we can apply the normal approximation for the sample mean

for n=14 or n =19 since the sample size is <30 we don't have enough evidence to conclude that the sample mean is normally distributed

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

hello from mrbilldoesmath!

answer:   x (x+6)^2, choice b

discussion:

factor x out of the equation:

x^3 + 12x^2 + 36x = x (x^2 + 12x + 36).

note that 6+6 = 12 and 6*6 = 36 so the above factors into:

x (x+6)^2

which is choice b

you,

mrb