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

for this case we have that by definition, the surface area of a cylinder is given by:

where:

r: it is the radius of the cylinder

h: it is the height of the cylinder

we can also rewrite it as:

where:

la: it's the lateral area

ba: area of the base

option a

large crystals result from very slow cooling.

evaporation of water: this would produce an evaporite which is a sedimentary rock. like a salt pan in a desert. not possible to have volcanic rocks originate this way.

crystalization in molten earth: slow cooling over time. (hundreds to millions of years)

crystalization at earth's surface: this results in fast cooling. (a few hours to a few months or years)

crystalization from cooling off hot water: that would be a hydrothermal deposit. while associated with volcanics they are not volcanic rocks themselves and usually occur fairly rapidly.