The scores of the students on a standardized test are normally distributed, with a mean of 500 and a standard deviation of 110 What is the probability that a randomly selected student has a score between 350 and 550 ? Use the portion of the standard normal table to help answer the question. z Probability 0 point 0 0 0 point 5 0 0 0 0 point 2 5 0 point 5 9 8 7 0 point 3 5 0 point 6 3 6 8 0 point 4 5 0 point 6 7 3 6 1 point 0 0 0 point 8 4 1 3 1 point 2 6 0 point 8 9 6 1 1 point 3 5 0 point 9 1 1 5 1 point 3 6 0 point 9 1 3 1
Convert each score to a z-score using z = (score − 500) / 110. For 350, z ≈ −1.36; for 550, z ≈ 0.45. The table gives P(Z ≤ 0.45) ≈ 0.6736 and P(Z ≤ −1.36) ≈ 1 − 0.9131 = 0.0869, so the probability between them is 0.6736 − 0.0869 = 0.5867, or about 59%. The correct choice is 59 percent.
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