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.

1. What is the probability that a randomly chosen cup of coffee will have more than 130 mg?
2. Less than 100 mg?
3. Between 90 mg and 150 mg?
4. 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?
5. 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

orchestra answered 1 year ago

Next > < Previous

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...

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...

For a random variable that is normally distributed, with μ = 80 and σ = 10,...

For a random variable that is normally distributed, with μ = 80 and σ = 10, determine the probability that a simple random sample of 25 items will have a mean between 78 and 85? a. 83.51% b. 15.87% c. 99.38% d. 84.13%

Suppose x is a normally distributed random variable with μ=30 and σ=5. Find a value of the...

Suppose x is a normally distributed random variable with μ=30 and σ=5. Find a value of the random variable x. (Round to two decimal places as needed.) p(x >): 0.95

1. Suppose that the random variable X is normally distributed with mean μ = 30 and...

1. Suppose that the random variable X is normally distributed with mean μ = 30 and standard deviation σ = 4. Find a) P(x < 40) b) P(x > 21) c) P(30 < x < 35) 2. A radar unit is used to measure speeds of cars on a motorway. The speeds are normally distributed with a mean of 90 km/hr and a standard deviation of 10 km/hr. What is the probability that a car picked at random is travelling...

Suppose x is a normally distributed random variable with μ=13 and σ=2. Find each of the...

Suppose x is a normally distributed random variable with μ=13 and σ=2. Find each of the following probabilities. (Round to three decimal places as needed.) a) P(x ≥14.5) b) P(x12.5) c) P(13.86 ≤ x ≤ 17.7) d) P(7.46 ≤ x ≤16.52) d) c)

Assume that the random variable X is normally distributed, with mean μ=50 and standard deviation σ=7....

Assume that the random variable X is normally distributed, with mean μ=50 and standard deviation σ=7. compute the probability. P(57≤X≤66)

The weight of a small Starbucks coffee is a normally distributed random variable with a mean...

The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 340 grams and a standard deviation of 11 grams. Find the weight that corresponds to each event. (Use Excel or Appendix C to calculate the z-value. Round your final answers to 2 decimal places.) highest 30 percent middle 70 percent highest 90 percent lowest 20 percent

The weight of a small Starbucks coffee is a normally distributed random variable with a mean...

The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 415 grams and a standard deviation of 23 grams. Find the weight that corresponds to each event. (Use Excel or Appendix C to calculate the z-value. Round your final answers to 2 decimal places.) a. Highest 20 percent b. Middle 60 percent to c. Highest 80 percent d. Lowest 15 percent

The weight of a small Starbucks coffee is a normally distributed random variable with a mean...

The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 350 grams and a standard deviation of 11 grams. Find the weight that corresponds to each event. (Use Excel or Appendix C to calculate the z-value. Round your final answers to 2 decimal places.) a. Highest 10 percent _________ b. Middle 50 percent _________to________ c. Highest 80 percent _________ d. Lowest 10 percent__________

Subjects