Statistics and Probability Answers

A word is to be formed using some or all the 8 letters.
P A N D E M I C
Find the total number of ways of forming the word if
a) The word is 8-letter long. The letters can be in any combinations. (3 marks)
b) The word is 7-letter long. The word must begin with a consonant. (5 marks)
c) The word is 2-letter long. (3 marks)
d) The word is 6-letter long. Both A and I must be chosen and placed next to one another. (7 marks)
e) The word is 9-letter long. State a reason for your answer.

Bag A consists of 40 balls, 20% of them are red, the rest of them are green. Bag B consists of 30 balls, 70% of them are red, the rest of them are green. A ball is taken at random from Bag A and put into Bag B. Then, a ball is then taken at random from Bag B. Find the probability of having a red ball eventually.

A telephone company wants to advertise that more than 30% of all its customers have more than two telephones. to support this ad, the company selects a sample of 200 customers and finds that 72 have more than two telephones. does the evidence support the ad? Use a = 0.05

(8.3.11) Park officials make predictions of times to the next eruption of a particular​ geyser, and collect data for the errors​ (minutes) in those predictions. The display from technology available below results from using the prediction errors to test the claim that the mean prediction error is equal to zero. Comment on the accuracy of the predictions. Use a 0.05 significance level. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.
Assuming all conditions for conducting a hypothesis test are​ met, what are the null and alternative​ hypotheses?

The display provided from technology available below results from using data for a smartphone​ carrier's data speeds at airports to test the claim that they are from a population having a mean less than 5.00 Mbps. Conduct the hypothesis test using these results. Use a 0.05 significance level. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.
Assuming all conditions for conducting a hypothesis test are​ met, what are the null and alternative​ hypotheses?

Twelve different video games showing violence were observed. The duration times of violence were​ recorded, with the times​ (seconds) listed below. Assume that these sample data are used with a 0.10 significance level in a test of the claim that the population mean is greater than 80 sec. If we want to construct a confidence interval to be used for testing that​ claim, what confidence level should be used for a confidence​ interval? If the confidence interval is found to be 21.3 sec < mu<188.1 ​sec, what should we conclude about the​ claim?
77,13,586,49,0,61,208,43,183,0,2,52
The confidence level should be ??% (Do not round)

(8.3.2) 28 different video games showing alcohol use were observed. The duration times of ​alcohol use(in seconds) were recorded. When using this sample for a t test of the claim that the population mean is greater than 86 ​sec, what does df​ denote, and what is its​ value?
The value of df is ?

4. At a certain university, students can choose one of 3 general areas of study. Twenty percent of the students are studying STEM, 45% are studying Social Sciences and the rest are studying Arts & Humanities. In addition, 15% of the STEM students and 40% of the Social Science students are involved in Greek life (in a sorority or fraternity). Only 35% of the Arts and Humanities students are NOT members of a sorority or fraternity. (***Similar to example 4***)What is the probability that a student....(a) studies Arts & Humanities? (b) studies STEM and is NOT involved in Greek life? (c) studies Arts & Humanities and is NOT involved in Greek life? (d) studies Social Sciences and is NOT involved in Greek life? (e) is involved in Greek life? (f) is not involved in Greek life?

. It is estimated that 4% of people who spend time in the woods will get Lyme disease. Of people with Lyme disease, the test to determine if you have it is will give a positive reading 97% of the time. Of people who do not have Lyme disease, the same test will give a negative rating of 92% of the time. Make a tree diagram for this problem and then answer the following questions. Find the probability that a) a person gets a positive reading b) a person gets a negative reading c) a person gets a positive reading and they have Lyme diseased) a person gets a negative reading and they have Lyme disease) a person gets a negative reading and they don’t have Lyme disease

This problem is about a fast-food business. As it turns out, 60% of their business is via the drive-through window, and 40% is counter-service. Data from the registers reveals that 70% of the transactions at the drive-through are via credit/debit cards, while 80% of the transactions at the counter are via credit/debit cards. (The other transactions are via cash.) What is the probability....A.that a random transaction uses cash? B.that a random transaction uses credit cards? C.that a transaction was a credit-card transaction and at the drive-through window? D.that a transaction was a cash transaction and was at the drive-through window? E.that a random transaction was at the counter? F.that a random transaction was at the drive-through window?