The mean contents of the population of soda cans produced by a certain manufactu

Question

The mean contents of the population of soda cans produced by a certain manufacturer is 11.9 ounces, with a standard deviation of 0.40 ounces. The cans say. "Contents - 12 ounces." a. What per cent of the cans are underfilled? b. What per cent of the cans are overfilled? c. The population mean can be adjusted. To what amount should it be adjusted in order to have 95% of the cans contain 12.00 ounces or more? d. Suppose the population mean is 12.10 ounces. What does the standard deviation have to be in order to have 95% of the cans contain 12.00 ounces or more? Pole Vault: Three women have cleared 5 metres. Yelena Isinbayeva was the first to clear 5.00 m (16 ft 43/4 in) on July 22, 2005. On March 2, 2013, Jenn Suhr cleared 5.02 m (16 ft 51/2 in) Indoors to become the second. Sandi Morris cleared 5.00 meters on September 9, 2016. You plan to compete in the pole vault some day soon. Your mean over your last 300 Jumps is 4.90 meters, with a standard deviation of 0.12 meters. a. What is the probability that you would dear 5.00 meters in one jump? b. What is the probability that your average of three jumps would be 5.00 meters or more? c. What is the probability that you would clear 5.00 meters in your best-of-three jumps? d. What is the probability that you would dear 5.00 meters in each of three consecutive Jumps? A population of watermelons has a mean weight of 8.00 pounds and a standard deviation of 1.00 pound. a. How large does a sample of these watermelons have to be in order for the standard error to be 0.05 pounds? b. What would you expect a sample of 100 of these watermelons to weigh? c. What is the probability that a sample of 100 of these watermelons would weigh more than 810 pounds? d. What is the probability that a sample of 100 of these watermelons would weight less than 780 pounds?

Explanation / Answer

3)

a) SE = s / sqrt(n)

0.05 = 1 / sqrt(n)

n = 400

b) n * mean = 100 * 8 = 800

c) mean = 100 * 8 = 800 , standard deviation = s * sqrt(n) = 1 * sqrt(100) = 10

P(X> 810)

z = ( x - mean) / std.deviation

= ( 810 - 800) / 10

= 1

Now, we need to find p(Z> 1)

P(X> 810) = p(Z> 1) = 0.1587

d)

P(X7 80)

z = ( x - mean) / std.deviation

= ( 780 - 800) / 10

= -2

Now, we need to find p(Z < -2)

P(X < 780) = p(Z < -2) = 0.0228

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