Statistics and Probability Answers

The acts in a talent competition consist of 4 instrumentalists, 10 singers, and 6 dancers. If the acts are ordered randomly, what is the probability that a dancer performs first?

1.    At Foodland Supermarket 45% of customers pay by credit card. Find the probability that in a randomly selected sample of fifteen customers.

a.    Exactly four pay by credit card

A new sneaker claims that it can make male athletes jump higher. A sample of 69 male athletes is asked to jump once with their own sneakers on and once wearing the new sneakers. The average jump increased by 5.03 inches with the new sneakers with a standard deviation of 2.53 inch(es). Find the lower bound of a 95% confidence interval.

"An electrical firm manufactures light bulbs that have a length of life that is normally distributed with mean equal to 778 hours and a standard deviation of 43 hours. Find the probability that a bulb burns between 755 and 892 hours. 

Reporting summary measures such as the mean, median, and standard deviation has become very common in modern life. Many companies, government agencies will report these descriptive measures of a variable, but they will rarely provide information on the shape of the distribution of that variable. In previous tutorials, you have learned some basic properties of some distributions that can help you to decide if a specific type of distribution is a good fit for a set of data. According to the National Diet and Nutrition Survey: Adults Aged 19 to 64, British men spend an average of 2.15 hours per day in moderate or high intensity physical activity. The standard deviation of these activity times for this sample was 3.59 hours. Can we infer that these activity times could follow a normal distribution? The following may provide an answer.

a. Sketch a normal curve marking the points representing 1, 2, and 3 standard deviations above and below the mean, and calculate the values at these points using a mean of 2.15 hours and standard deviation of 3.59 hours.

b. Examine the curve with your calculations. Explain why it is impossible for this distribution to be normal based on your graph and calculations.

c. Considering the variable being measured, is it more likely that the distribution is skewed to the left or that it is skewed to the right? Explain why.

d. Suppose that the standard deviation for this sample was 0.70 hours instead of 3.59 hours, which make it numerically possible for the distribution to be normal. Again, considering the variable being measured, explain why the normal distribution is still not a logical choice for this distribution. e. In your opinion, is there any difference between the term statistics and statistic?

1. The probabilities of a machine manufacturing 0, 1, 2, 3, 4, or 5 defective parts in one day are 0.75, 0.17, 0.04, 0.025, 0.01, and 0.005 respectively. Find the variance and standard deviation of the probability distribution.

Unit 5 deals with two types of discrete random variables, the Binomial and the Poisson, and two types of continuous random variables, the Uniform and the Exponential. Depending on the context, these types of random variables may serve as theoretical models of the uncertainty associated with the outcome of a measurement.

Give an example, USING YOUR OWN WORDS (NOT TEXT COPIED FROM THE INTERNET), of how either the Poisson or the Exponential distribution could be used to model something in real life (only one example is necessary). You can give an example in an area that interests you (a list of ideas is below). Give a very rough description of the sample space.

If you use an idea from another source, please provide a citation in the sentence and a reference entry at the end of your post. Include a citation even if you paraphrase from a website. Please do not copy blocks of text from the Internet--try to use your own words.

When forming your answer to this question you may give an example of a situation from your own field of interest for which a random variable, possibly from one of the types that are presented in this unit, can serve as a model. Discuss the importance (or lack thereof) of having a theoretical model for the situation. People can use models to predict business conditions, network traffic levels, sales, number of customers per day, rainfall, temperature, crime rates, or other such things.

1. An experiment consists of tossing a die and then flipping a coin once if the number of the dies is even. If the number on the die is off, the coin is flipped twice. Using notation 4H, for example, to denote the outcome that the die comes up 4 and then the coin comes up heads, and 3HT to denote the outcome that the dies comes up 3 followed by a head and then a tail on the coin, construct a three diagram to show the 18 elements of the sample space S.

In a survey of men in the United States (ages 20-29), the mean height was 69.6 inches with a standard deviation of 3.0 inches. Find the minimum height in the top 22%.

A present and a treasurer are to be chosen from a student club consisting of 50 people . How many different choices of officers are possible if

( 1 ) there are no restrictions ;

( 2 ) A will serve only if he is a president ;

( 3 ) B and C will serve together or not at all ;

( 4 ) D and E will not serve together ?