Question

find the z value such that 87% of the standard normal curve lies between -z ans z

Answer 1

87% area between -z and z means 100-87% = 13% area outside the -z and z range

we know that the distribution is symmetric, so we will have 13/2 = 6.5% on left hand side and 6.5% on right hand side.

6.5% means 6.5/100 = 0.065

Using the z distribution table for 0.065 or using excel function NORMSINV(probability)

we get

= NORMSINV(0.065)

= -1.51

This is the left tailed area, so right tailed area will be same, but with positive sign

So, left area is -1.51 and right area is 1.51

Therefore, 87% of the standard normal curve lies between -1.51 and 1.51