QUESTION 10
5 points + Sa
Find the critical value \( t_{C} \) for a \( 98 \% \) confidence level when the sample size is 20 . Use Table 4 on page A10 (Appendix).
A. 2.528
B. 2.539
C. 1.328
D. 1.325
QUESTION 11
10 points Save Answe
Assume that IQ scores are normally distributed with a mean of 100 and a standard deviation of 15 . If a sample of 70 people are selected, find the probability that the mean IQ score of the sample is greater than 102.
A. 0.447
B. 0.132
C. 0.868
D. 0.553
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Step 1 ：\(\text{For question 10}:\)

Step 2 ：\(\text{Step 1: Determine the degrees of freedom: } df = n - 1 = 20 - 1 = 19 \)

Step 3 ：\(\text{Step 2: Look up the critical value in the t-table for } df = 19 \text{ and } 98\% \text{ confidence level: } t_{C} = 2.539 \)

Step 4 ：\(\text{Answer 10:} 2.539\)

Step 5 ：\(\text{For question 11}:\)

Step 6 ：\(\text{Step 1: Calculate the standard error: } SE = \frac{\sigma}{\sqrt{n}} = \frac{15}{\sqrt{70}} \approx 1.7894 \)

Step 7 ：\(\text{Step 2: Calculate the z-score for the sample mean: } z = \frac{\bar{x} - \mu}{SE} = \frac{102 - 100}{1.7894} \approx 1.1174 \)

Step 8 ：\(\text{Step 3: Find the probability using the z-table that z-score is greater than 1.1174: } P(z > 1.1174) \approx 0.1319 \)

Step 9 ：\(\text{Answer 11:} 0.1319\)