Suppose x has a distribution with μ = 20 and σ = 19.
(a) If a random sample of size n = 42 is drawn, find μx, σx and P(20 ≤ x ≤ 22). (Round σx to two decimal places and the probability to four decimal places.)
μx = |
σx = |
P(20 ≤ x ≤ 22) = |
(b) If a random sample of size n = 68 is drawn, find
μx, σx
and P(20 ≤ x ≤ 22). (Round
σx to two decimal places and the
probability to four decimal places.)
μx = |
σx = |
P(20 ≤ x ≤ 22) = |
(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 ---Select--- the
same as smaller than larger than part (a) because of
the ---Select--- same larger smaller sample size.
Therefore, the distribution about μx
is ---Select---
a) μx = 20
= 2.93
P(20 < x < 22)
= P(0 < z < 0.68)
= 0.2524
b) μx = 20
= 2.30
P(20 < x < 22)
= P(0 < z < 0.68)
= 0.3073
c) smaller than; Larger
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