Statistics and Probability Answers

In a workshop, three robots, Q, R and S, are employed to make chairs

 Robot Q makes 25% of the chairs

Robot R makes 45% of the chairs

The remaining chairs are made by Robot S

 Evidence has shown that 2 percent of the chairs made by robot Q are defective, 3 percent of the chairs made by robot R, and 5 percent of the chairs made by robot S are defective

 (a) Construct a tree diagram that illustrates all possible outcomes and probabilities (5 marks)

 A chair is randomly selected.

 (b) What is the probability that the chair that robot Q made is defective                                           (1 marks)

 (c) What is the probability of findings a broken chair (2 marks)

 (d) Given that a chair is defective, what is the probability that it was not made by robot R

An anonymous caller told the police that he saw a hit and run incident and had briefly seen 

the number plate of the car. He knew that the number plate started with two letters – a B 

and an E – but could not remember the order. After the letters were four digits – 3, 4, 8 and 

9 – but again he could not remember the order. The four numbers were followed by the 

letter V. How many number plates will the police have to check to be sure of including the 

car involved in the hit and run incident?

Consider a value to be significantly low if its z score less than or equal to 

minus -2 or consider a value to be significantly high if its z score is greater than or equal to 2. A data set lists weights​ (grams) of a type of coin. Those weights have a mean of 

5.37494 g and a standard deviation of 0.05202 g. Identify the weights that are significantly low or significantly high.

Three cards are drawn in succession, without replacement (kartu tidak dikembalikan lagi), from an ordinary deck

of playing cards.

Find the probability that the event A1 ∩ A2 ∩ A3 occurs, where A1 is the event that the first card is a red ace, A2

is the event that the second card is a 10 or a jack, A3 is the event that the third card is greater than 3 but less

than 7.

The accompanying table shows proportions of adults in metropolitan areas, categorized as to whether they are public-radio contributors and whether or not they voted in the last election. Voted Yes Contributors 0.63 0.14 Non-contributors 0.13 0.10 No a. What is the probability that a randomly chosen adult from this population voted? b. What is the probability that a randomly chosen adult from this population contributes to public radio? c. What is the probability that a randomly chosen adult from this population did not contribute and did not vote?

A newspaper article estimated that the mean cost for preventive dental care was $165 per year. They indicated that the estimate was based on a sample of 100 people and that the margin of error was 2.8. Assuming a 95% confidence level was used, calculate the value of the standard error.

Suppose we wish to design a study to investigate the effects of loud music on teenagers’ ability to concentrate. We know from previous studies that the standard deviation of time to complete this task is 3.4 minutes. How many subjects would be required to ensure with 90% confidence that the generated estimate is within 1 minute of the true mean time required?

A consumer group is investigating a producer of diet meals to examine if its prepackaged meals actually contain the advertised 6 ounces of protein in each package. Based on the following data, is there any evidence that the meals do not contain the advertised amount of protein? Run the appropriate test at a 5% level of significance.

5.1

4.9

6.0

5.1

5.7

5.5

4.9

6.1

6.0

5.8

5.2

4.8

4.7

4.2

4.9

5.5

5.6

5.8

6.0

6.1

A journal article reported that the mean hospital stay following a particular surgical procedure in 2001 was 7.1 days. A researcher feels that the mean hospital stay in 2002 should be less due to initiatives aimed at reducing health care costs. A random sample of 40 patients undergoing the same surgical procedure in 2002 had a mean length of stay of 6.85 days with a standard deviation of 7.01 days. Run the appropriate statistical test at 𝛼 = 0.05