An intelligence scale for children is approximately normally distributed, with mean 100 and standard deviation 15. Complete parts (a) through (f) below. Click here to view page 1 of the standard normal distribution table, Click here to view page 2 of the standard normal distribution table. (a) What is the probability that a randomly selected test taker will score above 125? 0.0475 (Round to four decimal places as needed.) (b) What is the probability that a randomly selected test taker will score below 90? 0.2514 (Round to four decimal places as needed) (c) What proportion of test takers will score between 110 and 140? 0.2476 (Round to four decimal places as needed.) (d) Would it be unusual for a randomly selected child to have a score above 150? because $P(X > 150) =$ (Round to four decimal places as needed.) (e) What intelligence score will place a child in the 98th percentile? (Round to the nearest whole number as needed) (f) If normal intelligence is defined as scoring in the middle 95% of all test takers, determine the scores that differentiate normal intelligence from abnormal intelligence. Normal children score between and points. (Round to the nearest whole number as needed. Use ascending order.)
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To calculate the z-score, we use the formula: z = (x - Ī¼) / Ļ where: x is the given value, Ī¼ is the mean, Ļ is the standard deviation. Given values: For scoring above 125: x = 125 Ī¼ = mean (not given) Ļ = standard deviation (not given) For scoring below 90: x Show moreā¦
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