Respuesta :
Answer:
The minimum score a person must have to qualify for the society is 162.05
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
Test scores are normally distributed with a mean of 140 and a standard deviation of 15. This means that [tex]\mu = 140, \sigma = 15[/tex].
What is the minimum score a person must have to qualify for the society?
Since the person must score in the upper 7% of the population, this is the X when Z has a pvalue of 0.93.
This is [tex]Z = 1.47[/tex].
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.47 = \frac{X - 140}{15}[/tex]
[tex]X - 140 = 15*1.47[/tex]
[tex]X = 162.05[/tex]
The minimum score a person must have to qualify for the society is 162.05
