I understand how phiyp 095 what I have difficulty understan

I understand how phi(yp )= 0.95, what I have difficulty understanding is how does yp become 1.645. Other questions are how is phi(1.5) calculate to be 0.9332 or phi(-1) calculated to 0.1587.

Solution

You need to use the standard normal table to find y_p = 1.645 when it is given the probability is 0.95.

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When the probability is 0.9332, y_p =1.5 (from standard normal table)

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When the probability is 0.1587, y_p =-1 (from standard normal table)