Answer:
A 95% confidence interval for the population mean score for all bowlers in this league is [86.64, 94.48].
Step-by-step explanation:
Since in the question only 9 random scores are given, so I am performing the calculation using 9 random scores.
We are given that the scores of bowlers in particular league follow a normal distribution such that the standard deviation of the population is 6.
The accompanying data set of 9 random scores in ascending order is given as; 75, 86, 86, 88, 89, 93, 93, 98, 107
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = ~ N(0,1)
where, = sample mean score = = = 90.56
= population standard deviation = 6
n = sample of random scores = 9
= population mean score for all bowlers
<em>Here for constructing a 95% confidence interval we have used a One-sample z-test statistics because we know about population standard deviation.</em>
<u>So, 95% confidence interval for the population mean, </u><u> is ;</u>
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < < 1.96) = 0.95
P( < < ) = 0.95
P( < < ) = 0.95
<u>95% confidence interval for</u> = [ , ]
= [ , ]
= [86.64 , 94.48]
Therefore, a 95% confidence interval for the population mean score for all bowlers in this league is [86.64, 94.48].