Statistics and Probability Answers

Arun can solve 70% of a mathematics book while Anjali can 60% from the same book. If a problem is given to both of them identify the probability to solve the problem

Room\Reading <= 49 50 51 52 53 54<=
Bedroom 0.33 0.41 0.13 0.08 0.05 0
Kitchen 0.07 0.13 0.53 0.14 0.08 0.05
Living Room 0.06 0.09 0.13 0.28 0.33 0.11
a. What are the probabilities (that we are inside) for each room given that we obtain a reading of 53 (and assuming that we spend about equal amounts of time in each room – i.e., that the sample comes equally likely from any of the three rooms)?


b. For each reading we have our best guess (highest probability) determining which room we are in. What is our chance for being wrong when the reading is 53?


c. How would the result in B change if we knew that we are spending twice as much time in the bedroom than in the kitchen or living room (but the same in these two)?

a certain type of storage battery lasts on average 3 yeras with a standard deviation of 0.5 year.assuming that battery life is normally distributed find the probability that a given battery will lasts less than 2.3 years and between 2.5 years and 3.3 years

Ten competitors in a beauty contest were ranked by three judges as follows: Judges 2 3 4 5 6 7 A 6 10 3 10 2 7 8 9 10 9 B 5 8 9 7 1 2 7 8 9 1 C 4 9 7 10 2 3 9 7 3 9 7 7 Discuss which pair of judges have the nearest approach to common taste of beauty.

Assume that the college professor obtained a grant to study whether there was an improvement in the mathematics ability of freshmen. Using this grant money, he is able to obtain larger samples. The results are compiled in the following table.
Size of sample Average score Standard deviation
Last year 125
562 40
This year 100
568 42
Can the professor reject the null hypothesis that the average scores improved? Use a 5 % level of significance.

Blood glucose levels for obese patients have a mean of 100 with a standard deviation of 15. A researcher thinks that a diet high in raw cornstarch will have a positive or negative effect on blood glucose levels. A Sample of 30 patients who have tried the raw cornstarch diet has a mean glucose level of 140.
Test the hypothesis that the raw cornstarch had an effect.

A Field Poll Survey reported that 62% of registered voters in a state approved of allowing two people of the same gender to marry and have regular marriage laws apply to them. Among 18 to 39 year olds (registered voters in this state), the approval rating was 78%. Six in ten registered voters in this state said that the upcoming Supreme Court's ruling about the constitutionality of a proposition was either very or somewhat important to them. Out of those registered voters who support same-sex marriage, 71% say the ruling is important to them. In this problem, let the following apply.
• C = registered voters who support same-sex marriage
• B = registered voters who say the Supreme Court's ruling about the constitutionality of the proposition is very or somewhat important to them
• A = registered voters who are 18 to 39 years old.
1. Find P(C)= P(C|A)= P(C AND B

5.Suppose that 14 children, who were learning to ride two-wheel bikes, were surveyed to determine how long they had to use training wheels. It was revealed that they used them an average of nine months with a sample standard deviation of four months. Assume that the underlying population distribution is normal.
a. Construct a 99% confidence interval for the population mean length of time using training wheels.
(i) State the confidence interval
sketch the graph
calculate error bound