Question

In: Statistics and Probability

1) Every night there is a 20% chance that Mrs. Lemonde will let Mr.Lemonde’s dog George...

1) Every night there is a 20% chance that Mrs. Lemonde will let Mr.Lemonde’s dog George sleep in the bed. Using binomial distributions answer the following:

a) What is the probability that George sleeps with Mr. Lemonde exactly twice in one week? Explain

b) What is the probability that George sleeps with Mr. Lemonde at least once in one week?

Expert Solution

Every night there is a 20% chance that Mrs. Lemonade will let George sleep in the bed.

So, the probability that Mrs. Lemonade lets George sleep with her, on a randomly selected night, is 0.2.

And the chance that Mrs. Lemonade does not let George sleep with her, is (1-0.2), ie. 0.8.

Now, there are 7 nights in a week.

So, if X be the random variable, denoting the number of nights in a week when Mrs. Lemonade lets George sleep with her.

So, X follows binomial distribution, with parameters n=7, and p=0.2.

So, the probability mass function of X is

Where, i can take integer values from 0 to 7.

(a) We have to find the probability that George sleeps with Mrs. Lemonade twice in a week.

So, we have to find

So, the required probability is 0.2752.

(b) We have to find the probability that George sleeps with Mrs. Lemonade, at least once in a week.

So, we have to find

So, the required probability is 0.7903.

orchestra answered 1 year ago

In the following year, there is a 10% chance of a bear market, a 20% chance...

In the following year, there is a 10% chance of a bear market, a 20% chance of a bull market, and a 70% chance of a neutral market. Debt will return -2%, 5%, and 5% in the bear, bull and neutral market, respectively. Equity will return -15%, 15%, and 8% in the bear, bull and neutral market , respectively . What is the expected return of debt in %? (round to 1 decimal place) What is the volatility of equity in...

(1 point) In a certain community, 40% of the families own a dog, and 20% of...

(1 point) In a certain community, 40% of the families own a dog, and 20% of the families that own a dog also own a cat. It is also known that 36% of all the families own a cat. What is the probability that a randomly selected family owns a dog? What is the conditional probability that a randomly selected family doesn't own a dog given that it owns a cat?

1. If every stock has a 50% chance of increasing or decreasing at any given point...

1. If every stock has a 50% chance of increasing or decreasing at any given point in time, and you trade randomly, do you expect to break even? 2. You have sold short 500 shares of a stock, which is now trading for an ask/bid of $20.12/$20.10. If you want to limit your losses to 10% from this point, what type of order would you submit to the exchange? Does this guarantee you won’t lose more than 10%? 3. Explain...

Lilly is supposed to brush her teeth every night before going to bed. One night, her...

Lilly is supposed to brush her teeth every night before going to bed. One night, her dad asks herwhether she’s already brushed her teeth and she says “yes”. Lilly is usually truthful but to checkher dad touches her toothbrush and finds it dry.It is possible think about this story as a hypothesis test conducted by Lilly’s dad. Please carefullydescribe the following in complete english sentences in the context of this problem(a) The null hypothesis and the alternative hypothesis.(b) A type...

Posa Hotels, Inc., has a sixth night free policy. Every sixth night a guest stays at...

Posa Hotels, Inc., has a sixth night free policy. Every sixth night a guest stays at the hotel is free. Because not all guests stay enough nights to earn a free stay, on average the number of free nights redeemed is 70% of the maximum possible number of free nights available one obtains by dividing the total number of paid nights the hotel has had by 5. Rooms at Posa Hotels cost $300 per night. In 2019, Posa had a...

1. You own a share in Red Hat. Every period it has a 15 percent chance...

1. You own a share in Red Hat. Every period it has a 15 percent chance of going bankrupt. The interest rate is 0. If it survives to the end of the first period, it will pay $2 in dividends, $3 in dividends at the end of the second period, $3 in dividends at the end of the third period, and $4 in dividends at the end of the fourth period. It will pay no dividends after the end of...

1. A)You own a share in Red Hat. Every period it has a 15 percent chance...

1. A)You own a share in Red Hat. Every period it has a 15 percent chance of going bankrupt. The interest rate is 0. If it survives to the end of the first period, it will pay $2 in dividends, $3 in dividends at the end of the second period, $3 in dividends at the end of the third period, and $4 in dividends at the end of the fourth period. It will pay no dividends after the end of...

Your investment has a 20% chance of earning a 26% rate of return, a 50% chance...

Your investment has a 20% chance of earning a 26% rate of return, a 50% chance of earning a 15% rate of return and a 30% chance of losing 9%. What is your expected return on this investment? Enter answer in percents, accurate to two decimal places.

George invested $1,250 at the end of every month into an investment fund that was earning...

George invested $1,250 at the end of every month into an investment fund that was earning interest at 4.25% compounded monthly. He stopped making regular deposits at the end of 9 years when the interest rate changed to 4.50% compounded quarterly. However, he let the money grow in this investment fund for the next 4 years. a. Calculate the accumulated balance in his investment fund at the end of 9 years b. Calculate the accumulated balance in his investment fund...

1.A vendor prepares 100.00 hotdogs every day and sells at $18.00 /piece. For each hot dog,...

1.A vendor prepares 100.00 hotdogs every day and sells at $18.00 /piece. For each hot dog, he spends $10.00 in the raw material. Additionally he spends $1.02 for packing each hotdog and monthly $54.00, $21.00, $12.00 as food truck rent, electricity and other expenses respectively. On a particular day in June 114.00 people came wanting the hotdog. Vendor thinks $5.00 per lost sale. Determine vendor’s profit for that day? Assume there are 30 days in the month. 2. A restaurant...