Question

Suppose *x* has a distribution with *μ* = 22 and
*σ* = 18.

(a) If a random sample of size *n* = 35 is drawn, find
*μ*_{x}, *σ*_{x}
and *P*(22 ≤ *x* ≤ 24). (Round
*σ*_{x} to two decimal places and the
probability to four decimal places.)

μ_{x} = |

σ_{x} = |

P(22 ≤ x ≤ 24) = |

(b) If a random sample of size *n* = 60 is drawn, find
*μ*_{x}, *σ*_{x}
and *P*(22 ≤ *x* ≤ 24). (Round
*σ*_{x} to two decimal places and the
probability to four decimal places.)

μ_{x} = |

σ_{x} = |

P(22 ≤ x ≤ 24) = |

(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---
smaller than the same as larger than part (a) because of
the ---Select--- smaller larger same sample size.
Therefore, the distribution about *μ*_{x}
is ---Select--- wider narrower the same .

Answer #1

a) formula for the standard normal Z score :

b) n=60

c) The standard error is inversely proportional to the sample size

in b the sample size is large hence the standard error reduces, in the term the standard Z score increases in b compared to a.

Hence the probability of part b is higher than part a

Suppose x has a distribution with μ = 12 and
σ = 8.
(a) If a random sample of size n = 34 is drawn, find
μx, σx
and P(12 ≤ x ≤ 14). (Round
σx to two decimal places and the
probability to four decimal places.)
μx =
σx =
P(12 ≤ x ≤ 14) =
(b) If a random sample of size n = 58 is drawn, find
μx, σx
and P(12 ≤ x ≤ 14). (Round
σx...

Suppose x has a distribution with μ = 21 and
σ = 15.
(a) If a random sample of size n = 36 is drawn, find
μx, σx
and P(21 ≤ x ≤ 23). (Round
σx to two decimal places and the
probability to four decimal places.)
μx =
σx =
P(21 ≤ x ≤ 23) =
(b) If a random sample of size n = 60 is drawn, find
μx, σx
and P(21 ≤ x ≤ 23). (Round
σx...

Suppose x has a distribution with μ = 29 and
σ = 24.
(a)
If a random sample of size n = 31 is drawn, find
μx, σx
and P(29 ≤ x ≤ 31). (Round
σx to two decimal places and the
probability to three decimal places.)
μx=σx=P(29
≤ x ≤ 31)=
(b)
If a random sample of size n = 72 is drawn, find
μx, σx
and P(29 ≤ x ≤ 31). (Round
σx to two decimal places and...

Suppose x has a distribution with μ = 23 and σ = 15.
(a) If a random sample of size n = 32 is drawn, find μx, σ x and
P(23 ≤ x ≤ 25). (Round σx to two decimal places and the probability
to four decimal places.) μx = σ x = P(23 ≤ x ≤ 25) =
(b) If a random sample of size n = 73 is drawn, find μx, σ x and
P(23 ≤ x ≤...

Suppose x has a distribution with μ = 15 and σ = 12.
(a) If a random sample of size n = 32 is drawn, find μx, σ x and
P(15 ≤ x ≤ 17). (Round σx to two decimal places and the probability
to four decimal places.)
μx =
σ x =
P(15 ≤ x ≤ 17) =
(b) If a random sample of size n = 57 is drawn, find μx, σ x and
P(15 ≤ x ≤...

Suppose x has a distribution with μ = 25 and
σ = 22.
(a) If a random sample of size n = 40 is drawn, find
μx, σx
and P(25 ≤ x ≤ 27). (Round
σx to two decimal places and the
probability to four decimal places.)
μx =
σx =
P(25 ≤ x ≤ 27) =
(b) If a random sample of size n = 56 is drawn, find
μx, σx
and P(25 ≤ x ≤ 27). (Round
σx...

7. Suppose x has a distribution with μ = 29
and σ = 27.
(a) If a random sample of size n = 34 is drawn, find
μx, σx
and P(29 ≤ x ≤ 31). (Round
σx to two decimal places and the
probability to four decimal places.)
μx =
σx =
P(29 ≤ x ≤ 31) =
(b) If a random sample of size n = 62 is drawn, find
μx, σx
and P(29 ≤ x ≤ 31). (Round...

Suppose x has a distribution with ? = 11 and
? = 8.
(a) If a random sample of size n = 48 is drawn, find
?x, ?x
and P(11 ? x ? 13). (Round
?x to two decimal places and the
probability to four decimal places.)
?x =
?x =
P(11 ? x ? 13) =
(b) If a random sample of size n = 66 is drawn, find
?x, ?x
and P(11 ? x ? 13). (Round
?x...

Suppose x has a distribution with μ = 19 and σ = 15. (a) If a
random sample of size n = 48 is drawn, find μx, σ x and P(19 ≤ x ≤
21). (Round σx to two decimal places and the probability to four
decimal places.) μx = σ x = P(19 ≤ x ≤ 21) = (b) If a random sample
of size n = 58 is drawn, find μx, σ x and P(19 ≤ x ≤...

Suppose x has a distribution with μ = 29 and σ = 25.
(a) If a random sample of size n = 41 is drawn, find μx, σ x
and P(29 ≤ x ≤ 31). (Round σx to two decimal places and the
probability to four decimal places.)
μx =
σ x =
P(29 ≤ x ≤ 31) =
(b) If a random sample of size n = 71 is drawn, find μx, σ x
and P(29 ≤ x ≤...

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