9. ACT scores are normally distributed around a mean of 22, with a standard devi
ID: 2644248 • Letter: 9
Question
9. ACT scores are normally distributed around a mean of 22, with a standard deviation of 4. What proportion of the the population scored higher than 29? 10. Random variable X has a sample mean household income level = $4,000. It is normally distributed with sigma = $14,000. What is the required sample size required to get the margin of error of a 95% confidence interval to equal $500? 11. Nestor Milk Powder is sold in packets with an advertised mean weight of 1.5kg. The standard deviation is known to be 184 grams. A consumer group wishes to check the accuracy of the advertised mean and takes a sample of 52 packets finding an average weight of 1.49kgs. What is the set of hypotheses that should be use to test the accuracy of advertised weight? 12. Enough with the multiple choice questions!Explanation / Answer
9.
Z = (Observed Mean - Sample Mean) / Standard Deviation = (29-22) / 4 = 1.75
at this value of Z , Area covered = 1-.0401 = .9599 = 95.99% ( as per the chart of Z table)
10.
correct answer is
b. 3012
it is a two tail case , so at Confidence interval = 95% so in one side area is 47.5% or .475
Z.475 = 1.96 ( as per the chart of Z table)
Sample size = (Z.475* S.D. / 500)2 = (1.96*14000/500)^2 = 3011.81 = 3012 approx
11.
Correct set of Hypothesis is:
a. H0:u = 1.5 ; H1 : u ? 1.5
as null hypothesis means mean weight is 1.5 kg and
alternative hypothesis is mean weight is is not equal to 1.5 kg.
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