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Answer:
a) 0.8708 = 87.08% probability that x is less than 60
b) 0.9641 = 96.41% probability that x is greater than 16.
c) 0.8349 = 83.49% probability that x is between 16 and 60
d) 0.1292 = 12.92% probability that x is more than 60.
Step-by-step explanation:
When the distribution is normal, we use 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.
In this question, we have that:
a. x is less than 60
This is the pvalue of Z when X = 60. So
has a pvalue of 0.8708
0.8708 = 87.08% probability that x is less than 60
b. x is greater than 16
This is 1 subtracted by the pvalue of Z when X = 16. So
has a pvalue of 0.0359
1 - 0.0359 = 0.9641
0.9641 = 96.41% probability that x is greater than 16.
c. x is between 16 and 60
This is the pvalue of Z when X = 60 subtracted by the pvalue of Z when X = 16. We found those in a and b, si:
0.8708 - 0.0359 = 0.8349
0.8349 = 83.49% probability that x is between 16 and 60
d. x is more than 60
This is 1 subtracted by the pvalue of Z when X = 60.
So
1 - 0.8708 = 0.1292
0.1292 = 12.92% probability that x is more than 60.