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If the requirments of np > or equal 5 and nq > or equal to 5 are both satisfied, estimate the indicated probability by using the normal distribution; if  np< 5 or nq < 5, then state that the normal approximation should not be used. Use TI-84 caculator.

With  n =13 and p = 0.4, find P(fewer than 3).
asked Apr 2, 2015 in STATISTICS by doan12345 Pupil

1 Answer

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Step 1:

The number of samples n = 13.

Probability of success event p = 0.4.

Probability of failure event  q=1 - p =1 - 0.4 = 0.6.

First find np.

image

Now find nq.

image

Now image and image then estimate the indicated probability using normal distribution.

Find Mean.

Mean image

Mean of the event is 5.2.

Find Standard deviation.

Standard deviation image

Standard deviation of the event is image.

Step 2:

Find indicated probability image.

image.

Standardize x to z using z - Score formula.

z - Score formula is image,

where image is the random variable,

image is the mean and

image is the standard deviation.

image

From z - score table the probability is image.

image.

image.

Solution:

image.

Note:

Using TI-84 calculator,

You need to type in your calculator as shown below.

image

Then you will get image.

answered Apr 2, 2015 by Lucy Mentor

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