Question

In: Statistics and Probability

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?

Solutions

Expert Solution

Let X denotes the temperature of coffee served at a restaurant.

Approximately, we can write X ~ Normal(160, 5.42)

a) The probability that a coffee serving is between 153 and 167 degrees

The percentage of coffee servings are between 153 and 167 degrees = 100*0.8051 = 80.51%

b) The probability that a coffee serving is served at a temperature greater than or equal to 170 degrees

The percentage of coffee is served at a temperature greater than or equal to 170 degrees = 100*0.0320 = 3.2%

c)

orchestra answered 1 year ago
Next > < Previous

Related Solutions

The annual ground coffee expenditures for households are approximately normally distributed with a mean of $...
The annual ground coffee expenditures for households are approximately normally distributed with a mean of $ 46.64 and a standard deviation of $ 11.00 a. Find the probability that a household spent less than $30.00. b. Find the probability that a household spent more than ​$60.00. c. What proportion of the households spent between​$20.00 and ​$30​.00? d.97.5​% of the households spent less than what​ amount?
Suppose a restaurant determines that their daily profits are approximately normally distributed with a mean of...
Suppose a restaurant determines that their daily profits are approximately normally distributed with a mean of μ = $1500 and a standard deviation of σ = $1050. What is the probability that the restaurant makes a profit each day? In other words, what is the probability that the restaurant’s daily profit is at least one cent? Assuming that the standard deviation stays the same, what daily mean would be re- quired for there to be a 99% chance that the...
11.   The high temperature in Chicago for the month of August is approximately normally distributed with...
11.   The high temperature in Chicago for the month of August is approximately normally distributed with mean µ = 80 F and σ = 8 F. Draw a picture of the distribution, write the z-score, and use the appropriate notation. a.   What is the middle 99.7% of the data? b.   What is the probability that a randomly selected day in August has a temperature less than 78 F c.   What is the probability that the temperature is between 80o and...
1. The daily temperature in August in a region is normally distributed with a mean of...
1. The daily temperature in August in a region is normally distributed with a mean of 86 degrees F and a standard deviation of 4 degrees F. What is the probability (4 significant figures) that a daily temperature would be 72 degrees F or less? Would this be considered unusual, or not unusual? 2. The daily temperature in August in a region is normally distributed with a mean of 86 degrees F and a standard deviation of 4 degrees F....
1)The life in hours of a battery is known to be approximately normally distributed, with standard...
1)The life in hours of a battery is known to be approximately normally distributed, with standard deviation 1.25 hours. A random sample of 10 batteries has a mean life of 40.5 hours. A. Is there evidence to support the claim that battery life exceeds 40 hours ? Use α= 0.05. B. What is the P-value for the test in part A? C. What is the β-error for the test in part A if the true mean life is 42 hours?...
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.
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?
In a city, it is estimated that the maximum temperature in July is normally distributed with...
In a city, it is estimated that the maximum temperature in July is normally distributed with a mean of 23º and a standard deviation of 4°. Calculate the probability of having a maximum temperature between 20° and 28°     The amount of tea leaves in a can from a particular production line is normally distributed with μ (mean) = 110 grams and σ (Standard deviation) = 5 grams. If a sample of 9 cans is selected, what is the probability that...
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...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT