The roots of the equation 3x^2+2x+7=0
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Using the normal distribution, the indicated probability is given as follows:
P(7 ≤ x ≤ 11) = 0.6247.
<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:
P(7 ≤ x ≤ 11) is the <u>p-value of Z when X = 11 subtracted by the p-value of Z when X = 7</u>, hence:
X = 11:
Z = (11 - 8)/2
Z = 1.5
Z = 1.5 has a p-value of 0.9332.
X = 7:
Z = (7- 8)/2
Z = -0.5
Z = -0.5 has a p-value of 0.3085.
0.9332 - 0.3085 = 0.6247.
More can be learned about the normal distribution at brainly.com/question/28096232
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