Question

The scores on a short quiz in a statistics course were 0, 1, 2, …, 10 points depending on the number answered correctly out of 10 questions. The mean score was 5.9 and the standard deviation was 1.2. Assuming the scores are normally distributed, determine the percentage of students scoring 4 points. If using a TI83, TI-84, TI-89, or Excel show all commands. If using the table provided, use linear interpolation.

Answer 1

Sample size = n = 10

Mean = = 5.9

Standard deviation = = 1.2

We have to find P(X = 4)

Here we have to use continuity correction factor.

Therefor our probability becomes P( 4 - 0.5 < X < 4 + 0.5)

P( 4 - 0.5 < X < 4 + 0.5) = P( 3.5 < X < 4.5)

For this probability we have to find z score.

That is we have to find P( - 2 < Z < - 1.17)

P( - 2 < Z < - 1.17) = P(Z < - 1.17) - P(Z < - 2 ) = 0.121 - 0.0228 = 0.0983

( Usine excel =NORMSDIST(-1.17) - NORMSDIST(-2))