Answer :
Positive value of z, the probability that a standard normal variable is between 0 and Z, the value of Z is 1.16
Given that:
P(0<Z<z)= 0.3770
P(Z<z)- P(Z<z)= 0.3770
P(Z<z)=0.3770- P(Z<z)
P(Z<z)=0.3770+ 0.5000
{ we know that : P(Z<z)= P(Z<z)= 0.5}
P(Z<z)= 0.8770
so far calculating the value of Z, we look at the standard normal distribution table, we move to left until we reached first column we observe the value was 1.1 and then in the top value was observed we get the value that is 0.06. Then, we intersect the row and column we get the value of Z,
i.e, [1.1+ 0.06= 1.16]
Therefore P(Z≤1.16) = 0.8770
Learn more about Standard Normal distribution here:
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