Question

Hey guys 👋, can you help me to solve this problem please 🥺. Thank you 😊

1. The results of a mock board exam for assessing the mathematics skills of realtors were normally
distributed with a mean score of 72 and a standard deviation of 12. The realtors who scored in the
top 10% are to receive a special certificate, while those in the bottom 20% will be required to attend
a remedial workshop.
a. What score does a realtor need in order to receive a certificate?
b. What score will dictate that the realtor attend the workshop?

Answer 1

Hello????

Answer 2

Anyone can know?

Answer 3

the answer hehehe

Answer 4

general formula for the z-score of a value x with mean and standard deviation σ\[z=\frac{ x-x̄ }{ σ }\]

for part a) for the realtors in the top 10%, that means 90% of the other realtors scored below that. so to receive a certificate you must be in the 90th percentile.

use a z-table or calculator (I'll link one below) to calculate the z-score for the 90th percentile (0.90)

https://www.statology.org/percentile-to-z-score-calculator/

then plug that z-score into the z-score formula, along with the mean and standard deviation, to calculate the required score x

b) repeat this process for the 20th percentile