Name score julia 650 andrew 550 jason 380 cathy 720 jessica 710 robert 550 the table gives the scores of 6 students from a class of 25 in a competitive exam. the point estimate of the mean score for the students is . (round off your answer to the nearest tenth.)

The mean score for the students is 593.33.

Step-by-step explanation:

The table gives the scores of 6 students from a class of 25 in a competitive exam.

Name :  Julia     Andrew    Jason    Cathy    Jessica    Robert

Score :   650       550           380        720        710          550

Mean = Sum of the data values / Total number of data values    

Mean = ( 650 + 550 + 380 + 720 + 710 + 550 ) ÷ 6

= 3560 ÷ 6 =593.33

The mean score for the students is 593.33.

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.