If the statistician is right, what is the probability that the proportion of Rolls Royce owners in a sample of 508 Americans would differ from the population proportion by greater than 3%

The probability that the sample proportion would differ from the population proportion by greater than 3% is 0.008.

Step-by-step explanation:

The complete question is:

A statistician calculates that 7% of Americans own a Rolls Royce. If the statistician is right, what is the probability that the proportion of Rolls Royce owners in a sample of 508 Americans would differ from the population proportion by greater than 3%? Round your answer to four decimal places.

Solution:

Let the random variable X represent the number of Americans owning a Rolls Royce.

The proportion of Americans who own a Rolls Royce is, p = 0.07.

A random sample of n = 508 Americans were selected.

As the sample size is quite large, i.e. n = 508 > 30, according to the central limit theorem the sampling distribution of sample proportion would follow a normal distribution approximately.

The mean and standard deviation are as follows:

Compute the probability that the sample proportion would differ from the population proportion by greater than 3% as follows:

*Use the z-table.

Thus, the probability that the sample proportion would differ from the population proportion by greater than 3% is 0.008.

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step-by-step explanation:

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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