Mathematics, 06.06.2021 06:30 juliayaccarinoo

A bowling leagues mean score is 197 with a standard deviation of 12. The scores are normally distributed. What is the probability a given player averaged less than 190?m

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Answer from: jordantay208

0.281 = 28.1% probability a given player averaged less than 190.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

A bowling leagues mean score is 197 with a standard deviation of 12.

This means that $\mu = 197, \sigma = 12$

What is the probability a given player averaged less than 190?

This is the p-value of Z when X = 190.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{190 - 197}{12}$

Z = -0.58

Z = -0.58 has a p-value of 0.281.

0.281 = 28.1% probability a given player averaged less than 190.

Answer from: Quest

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step-by-step explanation:

Answer from: Quest

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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