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Using the normal distribution, it is found that the probabilities are given as follows:
a) 0.8871 = 88.71%.
b) 0.0778 = 7.78%.
c) 0.8485 = 84.85%.
<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.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation
.
The parameters in this problem are given as follows:
Item a:
The probability is the <u>p-value of Z when X = 1250 subtracted by the p-value of Z when X = 1000</u>, hence:
X = 1250:
By the Central Limit Theorem
Z = 1.42
Z = 1.42 has a p-value of 0.9222.
X = 1000:
Z = -1.81
Z = -1.81 has a p-value of 0.0351.
0.9222 - 0.0351 = 0.8871 = 88.71% probability.
Item b:
The probability is <u>one subtracted by the p-value of Z when X = 1250</u>, hence:
1 - 0.9222 = 0.0778 = 7.78%.
Item c:
The probability is the <u>p-value of Z when X = 1220</u>, hence:
Z = 1.03
Z = 1.03 has a p-value of 0.8485.
0.8485 = 84.85% probability.
More can be learned about the normal distribution at brainly.com/question/4079902
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