Question

In: Statistics and Probability

4) The caffeine content of a cup of coffee in the cafeteria is a normally distributed...

4) The caffeine content of a cup of coffee in the cafeteria is a normally distributed random variable with μ = 130 mg and σ = 30 mg. a) What is the probability that a randomly chosen cup of coffee will have more than 130 mg? b) Less than 100 mg? c) Between 90 mg and 150 mg? d) If the cup of coffee was the strongest 5% in caffeine content (hint: think about whether this would be above or below the mean), how many mgs of caffeine would it contain? e) If the cup of coffee was the weakest 10% in caffeine content (hint: think about whether this would be above or below the mean), how many mgs of caffeine would it contain?

Solutions

Expert Solution


Related Solutions

The caffeine content of a cup of coffee in the cafeteria is a normally distributed random...
The caffeine content of a cup of coffee in the cafeteria is a normally distributed random variable with μ = 120 mg and σ = 25 mg. What is the probability that a randomly chosen cup of coffee will have more than 130 mg? Less than 100 mg? Between 95 mg and 140 mg? If the cup of coffee was the strongest 10% in caffeine content (hint: think about whether this would be above or below the mean), how many...
The caffeine content of a cup of coffee in the cafeteria is a normally distributed random variable with μ = 130 mg and σ = 30 mg.
The caffeine content of a cup of coffee in the cafeteria is a normally distributed random variable with μ = 130 mg and σ = 30 mg. What is the probability that a randomly chosen cup of coffee will have more than 130 mg? Less than 100 mg? Between 90 mg and 150 mg? If the cup of coffee was the strongest 5% in caffeine content (hint: think about whether this would be above or below the mean), how many...
A coffee machine fills a cup automatically with a volume of coffee normally distributed with expectation...
A coffee machine fills a cup automatically with a volume of coffee normally distributed with expectation 2.2dl and standard deviation 0.3dl. The cups used can take a volume of coffee with expectation value 2.5 dl and standard deviation 0.45 dl. The volume of the coffee machine drops and the volume of a cup is independent. What is the probability of it accidentally overflowing with a cup?
Scenario A: If the price of coffee went from $2/cup to $4/cup, and you reduced your...
Scenario A: If the price of coffee went from $2/cup to $4/cup, and you reduced your consumption from 100 cups/month to 90 cups/month, what is the elasticity of demand? Scenario B:  If the price of coffee went from $2/cup to $4/cup, and you reduced your consumption from 100 cups/month to 40 cups/month, what is the elasticity of demand? Which scenario shows elastic demand and which shows inelastic demand?
A coffee machine dispenses normally distributed amounts of coffee with a mean of 12 ounces and...
A coffee machine dispenses normally distributed amounts of coffee with a mean of 12 ounces and a standard deviation of 0.2 ounce. If a sample of 9 cups is selected, find the probability that the mean of the sample will be between 11.9 ounces and 12.1 ounces. Find the probability if the sample is just 1 cup.
A coffee machine dispenses normally distributed amounts of coffee with a mean of 12 ounces and...
A coffee machine dispenses normally distributed amounts of coffee with a mean of 12 ounces and a standard deviation of 0.2 ounce. If a sample of 9 cups is selected, find the probability that the mean of the sample will be greater than 12.1 ounces. Find the probability if the sample is just 1 cup.
1. Coffee temperature ~ The temperature of coffee served at a restaurant is approximately normally distributed...
1. Coffee temperature ~ The temperature of coffee served at a restaurant is approximately normally distributed with an average temperature of 160 degrees and a standard deviation of 5.4 degrees. a. What percentage of coffee servings are between 153 and 167 degrees? Final Answer: _______________________ b. What percentage of coffee is served at a temperature greater than or equal to 170 degrees? Final Answer: _______________________ c. What is the cutoff for the coolest 20% of coffee servings at this restaurant?
A coffee shop claims that its fresh-brewed drinks have a mean caffeine content of 80 milligrams...
A coffee shop claims that its fresh-brewed drinks have a mean caffeine content of 80 milligrams per 5 ounces. A city health agency believes that the coffee shop’s fresh- brewed drinks have higher caffeine content. To test this claim the health agency takes a random sample of 100 five-ounce servings and found the average mean caffeine content of the sample was 87 milligrams with standard deviation of 25 milligrams. Does this provide enough evidence at the 1% significance level to...
Caffeine (C8H10N4O2) is a stimulant found in coffee and tea. A solution of caffeine in the...
Caffeine (C8H10N4O2) is a stimulant found in coffee and tea. A solution of caffeine in the solvent chloroform (CHCl3) has a concentration of 0.0490m. a. Calculate the percentage of caffeine by mass in the solution. b. Calculate the mole fraction of caffeine in the solution.
A person eats a grapefruit and drinks a large cup of coffee AND a cup of...
A person eats a grapefruit and drinks a large cup of coffee AND a cup of orange juice for breakfast (I guess they were thirsty). All these items are acidic! How will the respiratory and renal systems respond? Include a description of how the respiratory system detects the error signal and activates its response.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT