How find a value of the standard normal random variable.

(Multiple choice) Please choose one of the following options between A – D for questions 1 – 4 1. Use standard normal distribution to find P(z < -2.33 or z > 2.33) (A) 0.7888  (B) 0.0198 (C) 0.9809 (D) 0.0606 2. If the area to the left of a z-score is greater than 0.5, what must be true?

(A) z-score must be negative

(B) z-score must be equal to 0

(C) z-score must be positive

(D) z-score must be equal to 0.5

3. The volume of a soda dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.36 ounces & a standard deviation of 0.24 ounces. The company receives complaints from consumers who actually measure the amount of soda in the cans & can claim that the volume is less than 12 ounces. What proportion of the soda cans contains less than 12 ounces? \

(A) 0.4332

(B) 0.9332

(C) 0.5668

(D) 0.0668

4. To find a value of the standard normal random variable z, called z 0 , such that P(-z 0  ≤ z ≤ z 0 ) = 0.8262, which of the following is true?

(A) Find z = 0.83 on the z-table, then the answer is 0.2967

(B) Since this question provides the probability, not z, the answer must be found by working the problem in reverse. Since the probability refers to a symmetric interval around the mean, the probability 0.8262 must be divided in half. Next, 0.4131 is found on the inside of the table then go to the outside of the table to find that z must be 1.36. So P(-1.36 ≤ z ≤ 1.36) = 0.8262

(C) Find z = 0.83 on the z-table, then the answer is (0.2967 + 0.2967)

(D) Since this question provides the probability, not z, the answer must be found by working the problem in reverse. Since the probability is larger than 0.5000 we must first subtract 0.5000 from 0.8262 to get 0.3262. Next, 0.3262 (or what number is closest) is found on the inside of the table then go to the outside of the table to find that z must be 0.94. so P(-0.94 ≤ z ≤ 0.94) = 0.8262

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