(a) What is the probability that X is less than 1? (Sketch the density curve, sh

Question

(a) What is the probability that X is less than 1? (Sketch the density curve, shade the area that represents the probability, then find that area. Do this for part (c) also.)


(b) What is the probability that X is less than 0.5?

3. The Normal distribution with mean ? = 24.6 and standard deviation ? = 6.5 is a good description of the total score on a college admission test. This is a continuous probability model for the score of a randomly chosen student. Call the score of a randomly chosen student X for short.

(a) Find the probability of this event. (Round your answer to four decimal places.)

Choose a student in grades 9 to 12 at random and ask if he or she is studying a language other than English. Here is the distribution of results. (Assume that no student is studying more than one language other than English.) German All others None Language Probabilit 0.27 0.12 0.03 0.02 0.56 (a) Explain why this is a legitimate probability model. (Select all that apply) All events are disjoint. All probabilities are between 0 and 1 The probabilities sum to 0. The probabilities sum to 1 All probabilities are between 0 and 0.5 All probabilities are between -1 and +1 (b) What is the probability that a randomly chosen student is studying a language other than English? (c) What is the probability that a randomly chosen student is studying French, German, or Spanish?

Explanation / Answer

a) The probabilities sum to 1

All events are disjoint

b) The probability is 1 ? 0.56 = 0.44

c) The probability is 0.27+0.12+0.03 = 0.42

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