WWIIFanatic
contestada

In baseball, a player’s batting average is the proportion of times the player gets a hit out of his total number of times at bat. The distribution of batting averages in a recent season for Major League Baseball players with at least 100 plate appearances can be modeled by a Normal distribution with mean =0.261 and standard deviation =0.034 .
A player with a batting average below 0.200 is at risk of sitting on the bench during important games. About what percent of players are at risk?

1. 57.10%
2. 42.90%
3. 7.20%
4. 96.40%
5. 3.60%

Respuesta :

Answer: 3.60%

Explanation:

Using the normal distribution, it is found that 3.60% of players are at risk.

-------------

Normal Probability Distribution

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

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

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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.

-------------

  • Mean of 0.261 means that [tex]\mu = 0.261[/tex]
  • Standard deviation of 0.034 means that [tex]\sigma = 0.034[/tex].

The proportion of players with a batting average below 0.20 is the p-value of Z when X = 0.2, thus:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{0.2 - 0.261}{0.034}[/tex]

[tex]Z = -1.79[/tex]

[tex]Z = -1.79[/tex] has a p-value of 0.036.

0.036*100% = 3.60%

3.60% of players are at risk.

A similar problem is given at https://brainly.com/question/15181104

Otras preguntas