Question

Students' heights from Dorm A are normally distributed with a mean of 69.4 inches and standard deviation of 1.8 inches. Students heights from Dorm B are normally distributed with a mean of 71.6 inches and standard deviation of 1.7 inches. (You may consider these all to be population data.) A student is selected from one of the two dorms, but you don't know which one. At least how tall would that student need to be to have a probability of less than 0.03 of being from Dorm A? Round your answer to the second decimal place. If you cannot find the exact table entry you are looking for, use the value closest to the one you need. If there's a tie, use the smaller of the two possible entries.

please give step by step instructions on solution. The answer is 72.78 but im not sure how to do it.

Answer 1

First use z table to find the z score corresponding to 0.03

check values closest to 0.03 in the table. Closest values that I got are 0.0301 and 0.0294

0.0301 corresponds to -1.88 and 0.0294 corresponds to -1.89

selcting the closest value (0.0301), we get z = -1.88

we will take z as positive value for right tailed value.

so, z = 1.88

given that mean = 69.4 and standard deviation = 1.8 for Dorm A

using the formula

X value = mean + z*sd

= 69.4 + (1.88*1.8)

= 69.4 + 3.384

= 72.84