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Mazyrski [523]
3 years ago
11

An educational psychologist wishes to know the mean number of words a third grader can read per minute. She wants to make an est

imate at the 90% level of confidence. For a sample of 837 third graders, the mean words per minute read was 24.9. Assume a population standard deviation of 5.1. Construct the confidence interval for the mean number of words a third grader can read per minute. Round your answers to one decimal place.

Mathematics
2 answers:
brilliants [131]3 years ago
7 0

Answer: (24.6 , 25.2)

Step-by-step explanation:

Formula to find the confidence interval for population mean (\mu) is given by :-

\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}.

, where \overline{x} = Sample mean

z* = Critical z-value. (By z-table)

\sigma = Population standard deviation.

n= Sample size.

As per given , we have

\overline{x}=24.9

\sigma=5.1

n= 837

The critical value for 90% confidence interval : z* = 1.645 (By z-table)

The confidence interval for the mean number of words a third grader can read per minute will be :

24.9\pm (1.645)\dfrac{5.1}{\sqrt{837}}\\\\ 24.9\pm (1.645)(0.176281788104)\\\\=24.9\pm0.289983541431\\\\\approx24.9\pm0.3\\\\=(24.9-0.3,\ 24.9+0.3)\\\\=(24.6,\ 25.2)

∴  The confidence interval for the mean number of words a third grader can read per minute= (24.6 , 25.2)

Serga [27]3 years ago
4 0

Answer:we are 90% confident that

the mean number of words a third grader can read per minute is between 24 and 25

Step-by-step explanation:

Sample size n=837

Sample mean x bar= 24.9

Standard deviation , sigma= 5.1

And the formulae;

See attached picture for the solution.

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I think you meant 5,244 ÷ 6 = 874.

Answer/Step-by-step explanation:

We can check if this 5,244 ÷ 6 = 874 is correct by doing it opposite.

Since it 5,244 divide 6 we can do 874 x 6.

  \left[8   7   4] \\

×    [6]

======

+ 5244

=======

5244

Hence, this answer is correct.

[RevyBreeze]

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