Question

12. The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.3 inches. a) What is the probability that the average length of a steel sheet from a sample of 9 units is more than 29.95 inches long? Sketch the probability b) What is the probability that the average length of a steel sheet from a sample of 9 units is less than 29.7 inches long? Sketch the probability. 13. If we have a sample size of 100 and the mean of the population proportion (p) is 10, what is the mean and the standard deviation of the sampling distribution of the sample proportion? 14. The average salary computer scientists who subscribed to a web-based daily news update is known to be $46,816 with a population standard deviation of $12,557. Calculate a 91 percent confidence interval for the mean salary of 651 computer scientists.

Answer 1

13 let length of alominium - Coated sheets be clenoted by X. XaN(30.05, 0.3) 3~N( 30.05, 0.3/n), If Xa N(MG), I ^^ (1967) PCB = 24.05) = P Q > 7945) = P(2> 2995 ) W P(2> -) - 10(-) = 1-.1586553 = 0·8413447 where @l) is the odd og stendend Normal distilstion. P13224.7): PC -4 ( 29.7-M) - PL2419,753095) P(2435) - 0(-35) = 0.0002 32 13) 1.100, since it is the » PANC P: 0:10 case of Binomial proportion. (+2) n where , & p = 0.10 and n=100, y = 10 studos de inkome 4(2). Þ(1) 01 (1-0), 01704ova Mean= 0.10 Standard deviation O1X0.4 0.09 0-1 (1- 100 Joo sd = 0.0009 14 since it follows population sample size is king 1.651, 14² 46,81b, 8 = 12,557 Normal distribution. x N(46,816, 12557²)

Then confidence Interud for mean is gium sy Y I Z an in Zap 200 = 1.695348 (Calliduled in R) After substinting oldes 46816 † 1.6953 x 12557 √651 (45491.61, 47650.34)

> (29.95-30.05)/0.1 [1] -1 > pnorm(-1) [1] 0.1586553 > 1- pnorm(-1) [1] 0.8413447 > (29.7 - 30.05)/0.1 [1] -3.5 > pnorm(-3.5) [1] 0.0002326291 > abs(qnorm(0.09/2)) [1] 1.695398 > 46816 - 1.695398*(12557)/sqrt(651) [1] 45981.61 > 46816 + 1.695398*(12557)/sqrt(651) [1] 47650.39

R code for critical values and cdf is attached herewith