Question 1187603
a. z=(x-mean)/sd or (777-867)/50 or -1.8
and (987-867)/50 or 2.4
That probability that z is between those two is 0.9559

b. z > 137/50 or 2.74, with probability 0.0031

c. want z for 86th percentile and that is invnorm(0.86,0,1), or 1.08
1.08=(x-867)/50
x=921.

d. this is z>(887-867)/(50/sqrt(46) or 20*sqrt(46)/50 or 2.713, and that probability is 0.0033