Math Problem Statement
- Use the random variable notation to express symbolically each of the following:
X<0.9 An event in which the z-score of a randomly selected student is less than 0.9.
P(X<-1.3) The probability of an event in which the z-score of a randomly selected student is less than -1.3.
P(X<1.6)=0.94 The probability of an event in which the z-score of a randomly selected student is less than 1.6 is equal to 0.94.
- Use technology to find the probability that the z-score of a randomly selected student is:
i. less than 0.9:
(round the answer to 2 decimal places)
ii. more than -1.3:
(round the answer to 2 decimal places)
iii. between -2.2 and 1.7:
(round the answer to 2 decimal places)
iv. more than 9.5:
(round the answer to 2 decimal places)
v. less than 12.2:
(round the answer to 2 decimal places)
- Find the 40-th percentile:
= 0.40 (round the answer to 2 decimal places)
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Standard Normal Distribution
Z-scores
Percentiles
Formulas
P(X < z): Cumulative probability for a standard normal distribution
P(a < X < b): Probability between two z-scores
Percentile formula
Theorems
Empirical Rule (68-95-99.7)
Properties of the Standard Normal Distribution
Suitable Grade Level
Grades 11-12 (High School) or Introductory College Level
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