6. A national survey of small-business owners was conducted to determine the cha

Question

6. A national survey of small-business owners was conducted to determine the challenges for growth for their businesses. The top challenge, selected by 46% of the small-business owners, was the economy. A close second was finding qualified workers (37%). Suppose 15% of the small-business owners selected both the economy and finding qualified workers as challenges for growth. A small-business owner is randomly selected. What is the probability that the owner believes the economy is a challenge for growth if the owner believes that finding qualified workers is a challenge for growth as well?

7. If a coin is flipped is three times, what is the sample space and the probability of getting two tails?

8. According to an Access America survey, 30% said that it was cutting recreational driving. However, 27% said that it was consolidating or reducing errands. If these figures are true for all American drivers, and if 20 such drivers are randomly sampled and asked what is the first big change they made due to higher gas prices, what is the probability that exactly 8 said that it was consolidating or reducing errands?

9. The average fill volume of a regular can of soft drink is 12 ounces. Suppose the fill volume of these cans ranges from 11.97 to 12.03 ounces and is uniformly distributed. (a) What is the height of this distribution? (b) What is the probability that the fill volume is between 11.98 and 12.01 ounces?

10. According to the Internal Revenue Service, income tax returns one year averaged $1,332 in refunds for taxpayers and the standard deviation is $725. Assume that amounts owed or due on tax returns are normally distributed. (a) What proportion of tax returns show a refund greater than $2,000? (b) What proportion of the tax returns show a refund between $100 and $700?

Explanation / Answer

1). Let P(E) = People who think Economy is a challenge = 0.46

P(W) = People who think finding qualified worker is a challenge = 0.37

P(W and E) = People who think both economy and finding worker is a problem = 0.15

P(E/W) = People who think economy is a problem given that finding worker is a challenge to growth as well = P(W and E)/ P(W) + P(E) = 0.15/0.46+0.37 = 0.18

7). Sample Space = Different Combinations of Heads and Tails = (TTT, HHH, THT, TTH, HHT, HTT, HTH,THH)

Probability of Getting Two Tails = P(THT, HTT,HTH)/Total Sample = 3/8

8). Probabily that exactly 8 said it was recreational = nCrPrQn-r

We use this formula since this is a case of a Random Variable

N = 20 r=8 P= 0.27 Q=0.30
20C80.2780.3012

(20! / 8!12!)*(0.27^8 )*(0.30^12)

10). a). X = 1332

SD = 725

+-1 SD = 607 or 2057 = 0.64

We assume here that 1 SD = 0.34%

2 SD = 0.13

3 SD and beyond = 0.03

Thus, for a). 13% of tax returns show a refund greater than 2000

b). Now, since there are approximately 2 SDs between $100 and $700, we take this 13% of the cases where tax returns show a refund between $100 and $700

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