Respuesta :
Answer:
Probability that a student will score more than 1700 points is 0.50.
Step-by-step explanation:
We are given that the mean score for a standardized test is 1700 points. The results are normally distributed with a standard deviation of 75 points.
Let X = Scores results on a test
So, X ~ N([tex]\mu=1700,\sigma^{2} =75^{2}[/tex])
The z-score probability distribution for normal distribution is given by;
Z = [tex]\frac{ X -\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean score = 1700 points
[tex]\sigma[/tex] = standard deviation = 75 points
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.
So, the probability that a student will score more than 1700 points is given by = P(X > 1700 points)
P(X > 1700) = P( [tex]\frac{ X -\mu}{\sigma}[/tex] > [tex]\frac{1700-1700}{75}[/tex] ) = P(Z > 0) = 1 - P(Z [tex]\leq[/tex] 0)
= 1 - 0.50 = 0.50
Now, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0 in the z table which has an area of 0.50.
Hence, the probability that a student will score more than 1700 points is 50%.
