Question

9. At a large university, students have an average credit card debt of $2200 with a standard deviation of $600. 99.7% of all credit card debts are between what two numbers? Use the Empirical Rule, A) 1000, 3400 B) 1600, 2800 C) 31.6,58.3 D) 400, 4000 E) None of the Above 10. Find the percent of the Standard Normal model found in the given region: 1.9<z<2.11 B) 0.0065 A) 0.1618 C) 0.1667 D) 0.0113 E) None of the Above 11. A town's average snowfall is 30 inches per year with a standard deviation of 8 inches. How many standard deviations from the mean is a snowfall of 47 inches? A) 1.875 B) 2.125 C) 1.375 D) 1.75 E) None of the Above 12. Is the mean lifetime of a particular car engine at least 300,000 miles? To test this claim, a sample of 27 engines is measured, yielding an average of 295,450 miles and a standard deviation of 4200 miles. Use a significance level of 0.01 to test this hypothesis. A) IEETS B) NEETS C) IEETR D) NEETR E) None of the Above

Answer 1

Question-9

Here mean and standard deviation is given by,

$\therefore \mu=2200,\sigma=600$

From empirical rule we know that 99.7 % data lies between $(\mu-3\sigma,\mu+3\sigma)$

$\therefore (\mu-3\sigma,\mu+3\sigma)$

$\therefore (2200-3\times 600,2200+3\times 600)$

$\therefore (2200-1800,2200+1800)$

$\therefore (400,4000)$

Option (D) is correct answer.

Question-10

We need to find

$\therefore P(1.9<Z<2.11)$

$= P(Z<2.11)-P(Z\leq 1.9)$

$=0.9826-0.9713$

$=0.0113$

Option (D) is correct answer.

Question-11

Here the values are given by,

$\therefore \mu=30,\sigma=8$

We need to find how many standard deviation from the mean is snowfall of 47 inches.

i.e, we need to find the z score.

Here X=47

The value is z score is,

$\therefore Z=\frac{X-\mu}{\sigma}$

$\therefore Z=\frac{47-30}{8}$

$\therefore Z=\frac{17}{8}$

$\therefore Z=2.125$

Option (B) is correct answer.