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Question

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).

Answer 1

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.

Now find nq.

Now and then estimate the indicated probability using normal distribution.

Find Mean.

Mean

Mean of the event is 5.2.

Find Standard deviation.

Standard deviation

Standard deviation of the event is .

Step 2:

Find indicated probability .

.

Standardize x to z using z - Score formula.

z - Score formula is ,

where is the random variable,

is the mean and

is the standard deviation.

From z - score table the probability is .

.

.

Solution:

.

Note:

Using TI-84 calculator,

You need to type in your calculator as shown below.

Then you will get .