Question

Suppose \( x \) has a distribution with a mean of 80 and a standard deviation of 21 . Random samples of size \( n=36 \) are drawn. ? USE SALT (a) Describe the \( \bar{x} \) distribution and compute the mean and standard deviation of the distribution. \( \bar{x} \) has - Select-- \( \square \) distribution with mean \( \mu_{x}^{-}= \) \( \square \) and standard deviation \( \sigma_{\bar{x}}^{-}= \) \( \square \) (b) Find the \( z \) value corresponding to \( \bar{x}=73 \). \[ z= \] \( \square \) (c) Find \( P(\bar{x}<73) \). (Round your answer to four decimal places.) \[ P(\bar{x}<73)= \] \( \square \) (d) Would it be unusual for a random sample of size 36 from the \( x \) distribution to have a sample mean less than 73 ? Explain. Yes, it would be unusual because less than \( 5 \% \) of all such samples have means less than 73 . No, it would not be unusual because more than \( 5 \% \) of all such samples have means less than 73 . Yes, it would be unusual because more than \( 5 \% \) of all such samples have means less than 73 . No, it would not be unusual because less than \( 5 \% \) of all such samples have means less than 73.

          Suppose \( x \) has a distribution with a mean of 80 and a standard deviation of 21 . Random samples of size \( n=36 \) are drawn.
? USE SALT
(a) Describe the \( \bar{x} \) distribution and compute the mean and standard deviation of the distribution.
\( \bar{x} \) has - Select-- \( \square \) distribution with mean \( \mu_{x}^{-}= \) \( \square \) and standard deviation \( \sigma_{\bar{x}}^{-}= \) \( \square \)
(b) Find the \( z \) value corresponding to \( \bar{x}=73 \).
\[
z=
\]
\( \square \)
(c) Find \( P(\bar{x}<73) \). (Round your answer to four decimal places.)
\[
P(\bar{x}<73)=
\]
\( \square \)
(d) Would it be unusual for a random sample of size 36 from the \( x \) distribution to have a sample mean less than 73 ? Explain.
Yes, it would be unusual because less than \( 5 \% \) of all such samples have means less than 73 .
No, it would not be unusual because more than \( 5 \% \) of all such samples have means less than 73 .
Yes, it would be unusual because more than \( 5 \% \) of all such samples have means less than 73 .
No, it would not be unusual because less than \( 5 \% \) of all such samples have means less than 73.

Suppose x has a distribution with a mean of 80 and a standard deviation of 21 . Random samples of size n=36 are drawn.
? USE SALT
(a) Describe the x̅ distribution and compute the mean and standard deviation of the distribution.
x̅ has - Select– □ distribution with mean μx^-= □ and standard deviation σx̅^-= □
(b) Find the z value corresponding to x̅=73.

z=

□
(c) Find P(x̅<73). (Round your answer to four decimal places.)

P(x̅<73)=

□
(d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 73 ? Explain.
Yes, it would be unusual because less than 5 % of all such samples have means less than 73 .
No, it would not be unusual because more than 5 % of all such samples have means less than 73 .
Yes, it would be unusual because more than 5 % of all such samples have means less than 73 .
No, it would not be unusual because less than 5 % of all such samples have means less than 73.

Added by Joaquin A.

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