Answer: The sample mean
Step-by-step explanation:
The confidence interval is given by :-
Sample mean ± Margin of error
Given : The scores on a standardized test are normally distributed. If a random sample of standardized test scores is taken and the confidence interval is (497,537).
i.e. Sample mean - Margin of error = 497 ..(i)
Sample mean + Margin of error=537 ..(ii)
Adding (1) and (2), we get
2 (Sample mean) = 1034
⇒Sample mean = 517
Hence, the sample mean
Answer:
A score of 150.25 is necessary to reach the 75th percentile.
Step-by-step explanation:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
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.
A set of test scores is normally distributed with a mean of 130 and a standard deviation of 30.
This means that
What score is necessary to reach the 75th percentile?
This is X when Z has a pvalue of 0.75, so X when Z = 0.675.
A score of 150.25 is necessary to reach the 75th percentile.