Question

The final exam in a certain course has scores that are normally distributed with a mean of 82.4 with a standard deviation of 5.9. If 23 students are randomly selected, find the probability that the mean of their final exam scores is less than 84. Round your answer 4 places after the decimal point.

Answer 1

Solution :

Given that ,

mean = = 82.4

standard deviation = = 5.9

n = 23

= 82.4

=  / n = 5.9/ 23=1.23

P( <84 ) = P[( - ) / < (84-82.4) / 1.23]

= P(z <1.30 )

Using z table  

= 0.9032