How do you go about finding the z value when the percentage is already given? lo

Question

How do you go about finding the z value when the percentage is already given?

lo a63Hmwk R CUNY Login . Areas under x +1www.webassign.net/web/Student/Assignment.Responses.Submit CUNYOneSearchPearson Correlation Frequently Asked Q My LastPass VaultCUNY Login ? g8 Ca CUNY Virtual Deskt Need Help?W 10. 05/1 points 1 Previous Areswers Beunderstat2 6 3 023 Find the z value such that 87% of the standard normal curve lies between z -150 z and z (Round your answer to two decimal places. Sketch the area described. Type here to search 5 8 USE YOUR SH

Explanation / Answer

For a normal distribution,            

We Know that, P(X<-z)=P(X>z) [if X follows N(0,1)]

Let, consider ?% of standard normal curve lies between -z and z,

So,

P (-z < X < z) = ?/100

=> ? (z) - ? (-z) = ?/100

=> ? (z) – [1 - ? (z)] = ?/100

=> 2 ? (z)-1 = ?/100

=> z = ?-1 [ { ( ?/100 ) + 1 } /2]

So, i.e.

z = ?-1 [ { ( 87/100 ) + 1 } /2]

=1.514

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