Question

if I could get some help with better understanding this unit of statistics and probability it would be great. please and thank you!

DeroW.9 HourS? 29 Determining sample size. Refer to the previous rcise. You want to use a sample size such that about 95% of the averages fall within 5 minutes (0.08 hour) of the true mean 6.78. (a) Based on your answer to part (b) in Exercise 28 should the sample size be larger or smaller than 120? Explain. (b) What standard deviation of x do you need such that approximately 95% of all samples will have a mean within 5 minutes of u? (c) Using the standard deviation you calculated in pa rt (b), determine the number of students you need to sample.

Answer 1

Ans 28.

(a)

Standard Deviation of the average time

1.24 Standard Deviation of the average time - 120

Standard Deviation of the average time- 0.113

(b)

95% of sample means fall in the interval

$\mu \pm \frac{2\sigma}{\sqrt{n}}$

2.48 6.78 ± V120

(6.55,7.00)

(c)

P(X < 6.9) = P(Z < (6.9 - mean)/ standard error)

= P(Z < (6.9 - 6.78)/0.113)

= P(Z < 1.06)

= 0.8554 (from standard normal distribution table)

Ans 29

(a) Larger

(b) 5' = (5/60) hr = 0.083333 hrs ==> sample mean SD should be 1/2 of 0.083333

(c) 2*(1.24)/sqrt(n) = 0.083333

therfore, sqrt(n) = 2*(1.24)/ 0.083333

n = (29.7)^2 = 885.66 or 886