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# Probability, Means and Samples?

Topic: meaning of homework
June 26, 2019 / By Meriwether
Question: Hi, I'm stuck. Please Help. Red Tank , mean capacity = 6.5 gallons , standard deviation 0.5 Blue Tank , mean capacity = 22.4 gallons , standard deviation 0.5 Samples of 100 red tanks and 150 blue tanks were taken. What is the probability that the sample mean capacity of the red tanks is at least 15.8 gallons less than that of the blue tanks ? Actually, just noticed that I should typed standard deviation for red tank is 0.05 and for blue tank it was 0.07 But thanks for the help, I can make the amendments on my homework

## Best Answers: Probability, Means and Samples?

Les | 6 days ago
Tara Red Tank standard error = 0.5 / sqrt 100 = 0.05 Blue Tank standard error = 0.5 / sqrt 150 = 0.0408 Let's create a new random variable D (for difference) ... D = Blue - Red Mean of D is 22.4 - 6.5 = 15.9 Variance of D is 0.05^2 + 0.0408^2 = 0.00417 [yes, you always ADD variances] standard deviation of D = sqrt (0.00417) = 0.06455 Finally, we can find the answer ... P(D > 15.8) = P[z > (15.8 - 15.9) / 0.06455] = P(z > -1.55) now use the Standard Normal table ... P(z > -1.55) = 0.9394 hope that helped
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