Question

In: Math

Question 1 The coffee shop A coffee shop knows from past records that its weekly takings...

Question 1 The coffee shop A coffee shop knows from past records that its weekly takings (sales) are normally distributed with a mean of $10,500 and a standard deviation of $478. Answer the following questions:

a. Find the probability that in a given week the coffee shop would have takings of more than $10,700

b. Find the probability that in a given week the takings are between $9,800 and $11,000.

c. Calculate the inter-quartile range of weekly takings.

d. What are the maximum weekly takings for the worst 5% of weeks?

Question 2 Normal model

a. A cut-off score of 79 has been established for a sample of scores in which the mean is 67. If the corresponding z-score is 1.4 and the scores are normally distributed, what is the standard deviation?

b. The standard deviation of a normal distribution is 12 and 95% of the values are greater than 6. What is the value of the mean?

c. The mean of a normal distribution is 130, and only 3% of the values are greater than 155. What is the standard deviation?

Solutions

Expert Solution

solution: 1.

= 10500, = 478

a) P((X >10700)=?

z score =

P(X>10700) = 1 - value of z to the left of 0.42

P(X>10700) = 1 - 0.6628 = 0.3372

b) P(9800<X<11000)=?

Forget x= 9800

Z score =

For x= 11000

Z score =

P(9800<X<11000)= value of z to the left of 1.05 - value of z to the left of -1.46

P(9800<X<11000)=0.8531-0.0721 = 0.781

c) interquartile range = Q3-Q1

Q3= P75 and Q1= P25

Z score for P75 with 0.75 prob. from the z table = 0.67

Z score for P25 with 0.25 prob. from the z table = -0.67

Value of x at P75 = X= 10820

Value of x at P25= X= 10180

Interquartile range = 10820 - 10180 = 640

d) value of x at worst 5% of data=?

Value of z at0.05 from the z table = -1.64

Z score=

X= 9716

2.que.

a) z = 1.4, x= 79

Z score =

= 8.57

b) = 12, X= 6

95% values are greater than 6 it means 5% values are less than 6 so value of z score in z table from the left side with prob. 0.05 = -1.64

Z score =

= 25.68

c) = 130, X= 155

3% of the value are greater than 155.

So 97% of the values are less than 155

Value of z score from the z table from left of z with prob. 0.97 is 1.88

z score =

milcah answered 1 year ago
Next > < Previous

Related Solutions

Question 1 The coffee shop A coffee shop knows from past records that its weekly takings...
Question 1 The coffee shop A coffee shop knows from past records that its weekly takings (sales) are normally distributed with a mean of $10,500 and a standard deviation of $478. Answer the following questions: Find the probability that in a given week the coffee shop would have takings of more than $10,700 Find the probability that in a given week the takings are between $9,800 and $11,000. Calculate the inter-quartile range of weekly takings. What are the maximum weekly...
A company sells LED bulbs in packages of 20 for $25. From past records, it knows...
A company sells LED bulbs in packages of 20 for $25. From past records, it knows that a bulb will be defective with probability 0.01. The company agrees to pay a full refund if a customer finds more than 1 defective bulb in a pack. If the company sells 100 packs, how much should it expect to refund?
A music teacher knows from past records that 60% of students taking summer lessons play the...
A music teacher knows from past records that 60% of students taking summer lessons play the piano. The instructor believes that this proportion may have dropped due to the popularity of wind and brass instruments. A random sample of 80 students yielded 43 piano players. Use α = .05.
1. Alicia is the owner-operator of Cool Beans, a local coffee shop. For the past year,...
1. Alicia is the owner-operator of Cool Beans, a local coffee shop. For the past year, Cool Beans sold 215,000 drinks at an average price of $2.95 per serving. Her average variable cost per serving was $1.15. Currently, she has been using local TV and newspapers to generate interest and awareness at a cost of $171,000 per year. She recently contacted Brushfire Social Media and they estimated they could reach the same number of people in her community with a...
Question 1: A businesswoman is considering whether to open a coffee shop in a local shopping...
Question 1: A businesswoman is considering whether to open a coffee shop in a local shopping center. Before making this decision, she wants to know how much money people spend per week at coffee shops in that area. She took a random sample of 26 customers from the area who visit coffee shops and asked them to record the amount of money (in dollars) they would spend during the next week at coffee shops. At the end of the week,...
A researcher knows from the past that the standard deviation of the time it takes to...
A researcher knows from the past that the standard deviation of the time it takes to inspect a car is 16.8 minutes. A random sample of 24 cars is selected and inspected. The standard deviation is 12.5 minutes. At a= 0.05, can it be concluded that the standard deviation has changed? Use the P-value method. Assume the variable is normally distributed.
Question 16 The customers at Peete's coffee shop want to grab a quick cup of coffee...
Question 16 The customers at Peete's coffee shop want to grab a quick cup of coffee before boarding the Metra train into Chicago. The sign in the window promises "Quick, In-and-Out Service," and usually Peete's Coffee Shop keeps that promise. But one morning, customers were frustrated when the staff behind the counter showed more interest in gossiping about their social lives than in waiting on customers. Peete's coffee shop is suffering from a ________ gap.                 knowledge                 social expectations...
Alicia is the owner-operator of Cool Beans, a local coffee shop. For the past year, Cool...
Alicia is the owner-operator of Cool Beans, a local coffee shop. For the past year, Cool Beans sold 280,000 drinks at an average price of $2.92 per serving. Her average variable cost per serving was $1.40. Currently, she has been using local TV and newspapers to generate interest and awareness at a cost of $144,000 per year. She recently contacted Brushfire Social Media and they estimated they could reach the same number of people in her community with a social...
4. From past experience, the owner of a restaurant knows that, on average, 5% of the...
4. From past experience, the owner of a restaurant knows that, on average, 5% of the groups that make reservations never show, and 7% of the groups that make reservations show up late (the other 88% percent show up on time). a) How many reservations can the owner accept and still be at least 80% sure that all parties that make a reservation will show? b) How many reservations can the owner accept and still be at least 90% sure...
A CPA knows from past history that the average accounts receivable for a company is $521.72...
A CPA knows from past history that the average accounts receivable for a company is $521.72 with a standard deviation of $584.64. If the auditor takes a simple random sample of 100 accounts, what is the probability that the mean of the sample is within $120 of the population mean?
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT