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Using the normal distribution, the probabilities are given as follows:
a) 0.6517 = 65.17%
b) 0.0823 = 8.23%.
c) 0.6109 = 61.09%.
<h3>Normal Probability Distribution</h3>The z-score of a measure X of a normally distributed variable with mean and standard deviation
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
The mean and the standard deviation are given, respectively, by:
Item a:
The probability is the <u>p-value of Z when X = 10</u>, hence:
Z = 0.39
Z = 0.39 has a p-value of 0.6517.
0.6517 = 65.17% probability that the time is less than 10 minutes.
Item b:
The probability is the <u>one subtracted by the p-value of Z when X = 5</u>, hence:
Z = -1.39
Z = -1.39 has a p-value of 0.0823.
0.0823 = 8.23% probability that the time is more than 5 minutes.
Item c:
The probability is the <u>p-value of Z when X = 15 subtracted by the p-value of Z when X = 8</u>, hence:
X = 15:
Z = 2.18
Z = 2.18 has a p-value of 0.9854.
X = 8:
Z = -0.32
Z = -0.32 has a p-value of 0.3745.
0.9854 - 0.3745 = 0.6109 = 61.09%.
More can be learned about the normal distribution at brainly.com/question/4079902
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