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Use the standard normal distribution to find p(-2.50<z<1.50)
A study was done by an undergraduate student wanting to determine the probable location of computers (PC or laptop) in the home. The following probabilities were determined: Adult bedroom = 0.03, Child bedroom = 0.10, Other bedroom = 0.14, Home Office or Study room = 0.42, Other rooms = 0.31. What is the probability that a computer is not in the study?

10 babies are born in a hospital on the same day all weigh 2.8 KG each.what would be the standard deviation

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)?

How to find variance of a sample

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.
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