Calculate a normal interval probability and probabilities for two independent selections.

Calculate a normal interval probability and probabilities for two independent selections.

9 marks
ProbabilityQuestionBank.pdf

Intelligence Quotient (IQ) in a certain population is normally distributed with a mean of 100 and a standard deviation of 15.

  1. What percentage of the population has an IQ between 90 and 125?[2]
  2. If two persons are chosen at random from the population, what is the probability that both have an IQ greater than 125?[3]
  3. The mean IQ of a random group of 25 persons suffering from a certain brain disorder was found to be 95.2. Is this sufficient evidence, at the 0.05 level of significance, that people suffering from the disorder have, on average, a lower IQ than the entire population? State your null hypothesis and your alternative hypothesis, and explain your reasoning.[4]

Solution:

Solution locked

Sign in to view the step-by-step solution

Similar questions are unavailable for this question.
Answer:Test \(H_0:\mu=100\) against \(H_1:\mu<100\). The sample-mean standard deviation is \(15/\sqrt{25}=3\), so \(z=(95.2-100)/3=-1.60\). The one-tailed p-value is \(0.0548>0.05\); there is insufficient evidence that the mean IQ is lower.

Need help? Join our JC Math tuition classes.

Learn more