Respuesta :
Answer:
0.62% probability that a randomly selected person scores above 125 on the IQ test
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:
[tex]\mu = 100, \sigma = 10[/tex]
What is the probability that a randomly selected person scores above 125 on the IQ test
This is 1 subtracted by the pvalue of Z when X = 125. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{125 - 100}{10}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a pvalue of 0.9938
1 - 0.9938 = 0.0062
0.62% probability that a randomly selected person scores above 125 on the IQ test
Answer:
The probability that a randomly selected person scores above 125 on the IQ test is 0.0062.
Step-by-step explanation:
We are given that the the scores on an IQ test are approximately normally distributed with a mean of 100 and a standard deviation of 10.
Let X = scores on an IQ test
The z-score probability distribution is given by ;
Z = [tex]\frac{ X-\mu}{\sigma}} }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean score = 100
[tex]\sigma[/tex] = standard deviation = 10
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.
Now, the probability that a randomly selected person scores above 125 on the IQ test is given by = P(X > 125)
P(X > 125) = P( [tex]\frac{ X-\mu}{\sigma}} }[/tex] > [tex]\frac{ 125-100}{10}} }[/tex] ) = P(Z > 2.50) = 1 - P(Z [tex]\leq[/tex] 2.50)
= 1 - 0.9938 = 0.0062 The above probability is calculated using z table by looking at value of x = 2.50 in the z table which have an area of 0.99379.
Therefore, probability that a randomly selected person scores above 125 on the IQ test is 0.0062.
