use the standard normal distrubution to find P(-2.25 < z < 0)

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Expert Solution

Let Z be a random variable which follows standard normal distribution, then the probability distribution function is given by

Now the cumulative distribution function is given by

It is not easy to obtain the cumulative distribution function. Therefore generally Normal table is used for obtaining the property. For obtaining the probability of P(0<Z<a), just look at the normal probability table and the the area corresponding to coordinate a represents the corresponding probability. However there are certain probability which is converted into the desired probability by making use of certain probability given below.

Let us consider some property associated to normal distribution

1. P(Z<0)=P(Z>0)=0.5

2. P(-a<Z<0)=P(0<Z<a)

4. P(Z<a)=0.5+P(0<Z<a)

5. P(Z>a)=0.5-P(0<Z<a)

6 P(Z<-b)=P(Z>b)

For probability of P(-2.25<Z<0), we make use of the propert 3, and using this it is converted to the desired probability using the property 6 which is given below

Therefore the respective probability is 0.4878.

orchestra answered 1 year ago

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