Answer:
The z-score for this length is of 1.27.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
One-year-old flounder:
Mean of 127 with standard deviation of 22, which means that [tex]\mu = 127, \sigma = 22[/tex]
Anna caught a one-year-old flounder that was 155 millimeters in length. What is the z-score for this length
This is Z when X = 155. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{155 - 127}{22}[/tex]
[tex]Z = 1.27[/tex]
The z-score for this length is of 1.27.
