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Suppose x has a distribution with = 10 and 2. (a) If a random sample of size n = 49 is drawn, find μ, and P(10 ≤ x ≤ 12). (Round to two decimal places and the probability to four decimal places.) H = 10 x = 0.286 X P(10 ≤ x ≤ 12) = 0.4999 (b) If a random sample of size n = 55 is drawn, find and P(10 ≤ x ≤ 12). (Round o to two decimal places and the probability to four decimal places.) H = 10 x = 0.270 P(10 ≤ x ≤ 12) = X (c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).) The standard deviation of part (b) is smaller than ✓ part (a) because of the larger sample size. Therefore, the distribution about μ is narrower ✓

Suppose x has a distribution with = 10 and 2. (a) If a random sample of size n = 49 is drawn, find μ, and P(10 ≤ x ≤ 12). (Round to two decimal places and the probability to four decimal places.) H = 10 x = 0.286 X P(10 ≤ x ≤ 12) = 0.4999 (b) If a random sample of size n = 55 is drawn, find and P(10 ≤ x ≤ 12). (Round o to two decimal places and the probability to four decimal places.) H = 10 x = 0.270 P(10 ≤ x ≤ 12) = X (c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).) The standard deviation of part (b) is smaller than ✓ part (a) because of the larger sample size. Therefore, the distribution about μ is narrower ✓

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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Suppose x has a distribution with μ = 10 and o = 2. (a) If a random sample of size n = 49 is drawn, find μ Mx = = 10 0x = == 0.286 X P(10 ≤ x ≤ 12): = 0.4999 (b) If a random sample of size n = 55 is drawn, find μ, o and P(10 ≤ x ≤ 12). (Round o to two decimal places and the probability to four decimal places.) Mx= = 10 = 0.270 0 and P(10 ≤ x ≤ 12). (Round σ to two decimal places and the probability to four decimal places.) X X P(10 ≤ x ≤ 12) = (c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).) The standard deviation of part (b) is smaller than part (a) because of the larger sample size. Therefore, the distribution about is Mx ↑ narrower ↑
Transcribed Image Text:Suppose x has a distribution with μ = 10 and o = 2. (a) If a random sample of size n = 49 is drawn, find μ Mx = = 10 0x = == 0.286 X P(10 ≤ x ≤ 12): = 0.4999 (b) If a random sample of size n = 55 is drawn, find μ, o and P(10 ≤ x ≤ 12). (Round o to two decimal places and the probability to four decimal places.) Mx= = 10 = 0.270 0 and P(10 ≤ x ≤ 12). (Round σ to two decimal places and the probability to four decimal places.) X X P(10 ≤ x ≤ 12) = (c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).) The standard deviation of part (b) is smaller than part (a) because of the larger sample size. Therefore, the distribution about is Mx ↑ narrower ↑
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