Question

in a class of 40 students, each student conducts an experiment in which they spin a spinner and measure the final angle of the pointer. let the random variable X represent the mean of the angles found by the students. write the distrabution of X

Answer 1

When a spinner is spun, the possible angle is uniformly distributed from a = 0 to b = 360

Mean value of angle, = (a + b)/2

= (0 + 360)/2

= 180

Standard deviation, =

=

= 103.923

There are 40 students. So, from this distribution, a sample with size, n = 40 is taken.

According to central limit theorem, Distribution of X, which is the sampling distribution of mean will be normally distributed.

Mean of X, = = 180

=

=

= 16.432

Probability distribution of X = N(180, 16.432)