Question

Percentage grades in a large biology class follow a normal distribution with standard deviation 8.3. It is known that 20% of students receive grades higher than 77.97. What is the mean grade in the class?

Answer 1

80% of the class must receive a grade of 77.97 or less.
The z-score for 0.8 is 0.842
\[z=\frac{x-\mu}{\sigma}\]
\[0.842=\frac{77.97-\mu}{8.3}\ .........(1)\]
Now you need to solve equation (1) to find the mean grade mu.

Answer 2

hey the mean shud be 84.9586 right.. but how did u get 0.842 for 0.8... isnt it 0.7881.. im confused here..

Answer 3

thanks anyway :)

Answer 4

the mean should be less than 77.97. you have to do a table look up to find the corresponding z-score. or claculator

Answer 5

No, the mean must be less than 77.97. How did you get the result of 84.9586 for the mean? Your result is not the solution of equation (1) that I posted.
To find the appropriate z-score for a cumulative probability of 0.8 you need a standard normal distribution table. You need to find the value of z that will give a cumulative probability of 0.800. The value of z for a cumulative probability of 0.800 is 0.842.

Answer 6

oops sorry i mean 70.9814.. i summed it up instead of subtracting.. and okay hold on let me try to figure it out.. i know its 0.8 because its 1-0.2 right.. so i will have to look for the closest P value of 0.800 and then see the corresponding value for z right..? which is 0.84

Answer 7

awesome!

Answer 8

Good work! Your latest result is correct :)

Answer 9

thanks alot :) i have another question tho :(
One student received a grade of 75.9 in chemistry, a grade of 80.96 in biology, and a grade of 78.9 in physics. In which class did the student to the best, relative to other students in the class?

A. Chemistry

B. Biology

C.Physics

D. The student did equally well in all three classes relative to other students.

the answer i chose is A.. but correct me if im wrong..

Answer 10

need more info

Answer 11

insufficient data i guess.. the mean for chemistry is 66 and the mean for physics is 62

Answer 12

yeah i figured.. sorry..

Answer 13

need the std devs too

Answer 14

oh okay.. chemistry: mean=66 std dev.=9
biology: mean=70.98 std.dev=8.3
physics: mean=62 std.dev=12.99

Answer 15

compute the z-score for each and the highest z-score wins!

Answer 16

chem=1.10 bio=1.20 phy=1.30 so the answer is physics?

Answer 17

i guess so... i didn't compute them but trust you did it correctly

Answer 18

its z=(X-mean)/std.dev . right? if so then i should be right

Answer 19

yep, and your answers sound about right.

Answer 20

I checked. Your z-scores are all correct :)

Answer 21

alright thanks alot! @pgpilot326 and @kropot72 :D

Answer 22

you're welcome!

Answer 23

You're welcome :)

Answer 24

Percentage grades in a large biology class follow a normal distribution with standard deviation 8.3. It is known that 20% of students receive grades higher than 77.97. What is the mean grade in the class?
i got incorrect for the answer 70.9814 :s

Answer 25

i got 70.998 using .84 as my z-score. the z-score will vary depending upon what you use (calculator, table with differeing degrees of precision). try to use the tables they give you or whichever methods they suggest.

Answer 26

okay thanks.. it was my last attempt anyway.. but its okay at least i learnt something :) thanks and goodnight (its 3.01am in where i live)

Answer 27

buenos nochas! it's 1:01 here and I'm tired too

Answer 28

@amistre64
ok so @Hashir and @evilmath are just going to each room, calling the other one, and then giving each other medals