Question

In: Statistics and Probability

For a standard normal distribution, find: P(-1.64 < z < -1.48)

For a standard normal distribution, find:

P(-1.64 < z < -1.48)

Solutions

Expert Solution

We can solve this using two methods and using two different types of standard normal tables.

P(-1.64 < z < -1.48)

METHOD 1:

For finding P(-1.64 < z < -1.48)

we can use the standard normal table in which entries are negatives z or can be said as the entries which cover the left side of the curve which is less than the center of the curve.

The area under the curve areas:

Thus, P(-1.64 < z < -1.48) can be written as:

So, from the standard normal table, we get:

NOTE: Remember we have to use the standard normal table in which all Z entries are negative.

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METHOD 2:

Now, we will use the standard normal table which all Z positive entries.

So,

This can be written as

Now, can be found using a formula that:

(Total area under the curve is equal to 1)

So, from standard normal table

Similarly,

we can find:

So, we get:

Thus, we get:

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You can use any method which you feel more comfortable.


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