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What is the z-score of sample X, if #n = 169, mu= 33, St. Dev. =39, and E[X] =37#?

Answer 1

Emery Adams

The z-score is #=1.33#

The z-score of a sample mean is

#z=(barx-mu)/(sigma/sqrtn)#

Here.

#barx=E [X]=37 #

#mu=33#

#sigma=39#

#n=169#

#z=(37-33)/(39/sqrt169)#

#=4/(39/13)=4/3=1.33#

Hope this wil help!

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Answer 2

Josiah Allen

The z-score of a sample is calculated using the formula:

[ z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} ]

where:

( \bar{x} ) is the sample mean (E[X]),
( \mu ) is the population mean,
( \sigma ) is the population standard deviation, and
( n ) is the sample size.

Given that ( n = 169 ), ( \mu = 33 ), ( \sigma = 39 ), and ( E[X] = \bar{x} = 37 ):

[ z = \frac{37 - 33}{39 / \sqrt{169}} ]

[ z = \frac{4}{39 / 13} ]

[ z = \frac{4}{3} ]

[ z = 1.33 ]

The z-score of sample X is 1.33.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.