Question 761465: I am having trouble on these two problems..
Students in a particular class complete an exam in a mean time of 45 minutes with a standard deviation of 8 minutes. If student is selected at random, what is the probability he/she will complete it in less than 40 minutes?
An insurance company claims that a customer can save an average of at least $400 per year on car insurance. A sample of 22 customers showed that the mean amount saved was $375 per year with a standard deviation of $48. Use a level of significance of 0.01 to test the insurance company’s claim.
Thanks alot!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Students in a particular class complete an exam in a mean time of 45 minutes with a standard deviation of 8 minutes. If student is selected at random, what is the probability he/she will complete it in less than 40 minutes?
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z(40) = (40-45)/8 = -5/8
P(x < 40 min) = P(z < -5/8) = normalcdf(-100,-5/8) = 0.2660
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An insurance company claims that a customer can save an average of at least $400 per year on car insurance. A sample of 22 customers showed that the mean amount saved was $375 per year with a standard deviation of $48. Use a level of significance of 0.01 to test the insurance company’s claim.
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Ho: u < 400
H1: u >= 400 (claim)
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t(375) = (375-400)/[48/sqrt(22)] = -2.4429
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p-value = P(x-bar >= 400) = P(t >= -2.4429 when df = 21) = tcdf(-2.4429,100,21)
= 0.9883
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Conclusion: Since the p-value is greater than 1%, fail to reject Ho.
The test results do not support the claim.
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cheers,
Stan H.
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