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Using z-scores, it is found that the value of z is z = 1.96.
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Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula, which for a measure X, in a distribution with mean and standard deviation
, is given by:
- It measures how many standard deviations the measure is from the mean.
- Each z-score has an associated p-value, which is the percentile.
- The normal distribution is symmetric, which means that the middle 95% is between the <u>2.5th percentile and the 97.5th percentile</u>.
- The 2.5th percentile is Z with a p-value of 0.025, thus Z = -1.96.
- The 97.5th percentile is Z with a p-value of 0.975, thus Z = 1.96.
- Thus, the value of Z is 1.96.
A similar problem is given at brainly.com/question/16965597
Answer:
<em>Riley has 72 tokens</em>
Step-by-step explanation:
<u>System of Equations </u>
We have two conditions for the tokens Riley and Erik have earned. Let's call x and y to the number of tokens of Riley and Erik respectively. The first condition states that
Solving for y
The second condition is that the ratio of the number of tokens that Riley had to the number of tokens that Erik has is 8 to 7. It's written as
Or equivalently
Replacing y from the first equation
Operating
Simplifying
Riley has 72 tokens