Respuesta :
Answer:
b) 6.68%
Step-by-step explanation:
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.
The mean score on the scale is 50. The distribution has a standard deviation of 10.
This means that [tex]\mu = 50, \sigma = 10[/tex]
Matthew scores a 65. What percentage of people could be expected to score the same as Matthew or higher on this scale?
The proportion is 1 subtracted by the p-value of Z when X = 65. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{65 - 50}{10}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a p-value of 0.9332.
1 - 0.9332 = 0.0668
0.0668*100% = 6.68%
So the correct answer is given by option b.
