Given a normal distribution with ? = 100 and ? = 10, complete parts (a) through (d). Click here to view page 1 of the cumulative standardized normal distribution table. Click here to view page 2 of the cumulative standardized normal distribution table. a. What is the probability that X > 75? The probability that X > 75 is 0.9938 . (Round to four decimal places as needed.) b. What is the probability that X < 85? The probability that X < 85 is 0.0668 . (Round to four decimal places as needed.) c. What is the probability that X < 80 or X > 105? The probability that X < 80 or X > 105 is . (Round to four decimal places as needed.)
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For X > 75, the z-score is: z = (75 - 100) / 10 = -2.5 For X < 85, the z-score is: z = (85 - 100) / 10 = -1.5 For X < 80, the z-score is: z = (80 - 100) / 10 = -2 For X > 105, the z-score is: z = (105 - 100) / 10 = 0.5 Now, we can use the cumulative Show moreā¦
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Given a normal distribution with Ī¼ = 100 and Ļ = 10, complete parts (a) through (d). a. What is the probability that X > 70? The probability that X > 70 is .9986. (Round to four decimal places as needed.) b. What is the probability that X < 95? The probability that X < 95 is .3085. (Round to four decimal places as needed.) c. What is the probability that X < 85 or X > 115? The probability that X < 85 or X > 115 is .1336. (Round to four decimal places as needed.) d. 80% of the values are between what two X-values (symmetrically distributed around the mean)? 80% of the values are greater than and less than . (Round to two decimal places as needed.)
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