Verified answer

The first step in this problem is to find .8000 in a z-table. This proportion is the same as 80%. While you may notice there is no probability on the table that is exactly .8000, at z=.84, the probability is .7995. There are no probabilities on the table that are closer to .8000 than this.

From the value z=.84, we know that the answer is .84 standard deviations above the mean. To calculate the answer, we take the mean and add .84 times the standard deviation:

180+.84*20=196.8

80% of the data in a data set with mean 180 and standard deviation 20 lies under 196.8.

I'm not sure whether 196.8 constitutes 1.) 196 being right, or whether 4.) none of these is the answer because 196.8 rounds up to 197.

196 is the closest at about 78.8%

Depending on how accurate an answer they are looking for it is either

1.) 196

or 4.) none of these.

corresponding z value is 0.835

putting into equation x= (zx[s.d.])+mean

=(0.835x20)+180

= 196......................a