IXL - Find confidence intervals for population means (Precalculus practice)

A random sample of size 125 is drawn from a large population. The population standard deviation is 3.2. The sample mean is 32.9.

Find a

95%

confidence interval for the population mean,

𝜇

Round your answers to the nearest tenth.

𝜇

ref_doc_title.

Learn with an example

question

A random sample of size 900 is drawn from a large population. The population standard deviation is 2.3. The sample mean is 23.7.

Find a

90%

confidence interval for the population mean,

𝜇

Round your answers to the nearest tenth.

𝜇

key idea

You can use a random sample to calculate a

confidence interval for the population mean. The population mean is the mean of all data values in a population.

A confidence interval may or may not contain the population mean. A

confidence interval will contain the population mean for

of random samples whose elements were chosen randomly and independently.

The

confidence interval for the population mean,

𝜇

has endpoints

𝜎

where:

n
is the sample size.
𝜎
is the population standard deviation.
x
is the sample mean.
z
is the critical value for the confidence level
c
%
.
It is the
z
-value
for which the interval from
–
z
to
z
is the middle
c
%
of the standard normal distribution.
c
%
–
z
z
Here are some common critical values:
Confidence level,
c
%
Critical value,
z
90%
1.645
95%
1.960
99%
2.576

solution

Start by listing the given information:

The sample size is
n
=
900
.
The population standard deviation is
𝜎
=
2.3
.
The sample mean is
x
=
23.7
.
The critical value for a
90%
confidence level is
z
=
1.645
.

Use these values to find the endpoints of a

90%

confidence level for the population mean,

𝜇

𝜎

23.7

1.645

2.3

900

𝜎

23.7

0.126116…

The left endpoint is:

23.7

–

0.126116…

23.573883…

Round to the nearest tenth

≈

23.6

Round to the nearest tenth

The right endpoint is:

23.7

0.126116…

23.826116…

Round to the nearest tenth

≈

23.8

Round to the nearest tenth

So, a

90%

confidence interval for the population mean is:

23.6

𝜇

23.8

Looking for more? Try this:

$Confetti$

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Teacher tools

Work it out

Not feeling ready yet? These can help:

EE.5Find z-values

EE.7Distributions of sample means

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Confidence level, c %	Critical value, z
90%	1.645
95%	1.960
99%	2.576