Albert thinks that he has a special relationship with the number 3. In particular, Albert thinks that he would roll a 3 with a fair 6-sided die more often than you'd expect by chance alone. Suppose ? is the true proportion of the time Albert will roll a 3. (a) State the null and alternative hypotheses for testing Albert's claim. (Type the symbol "p" for the population proportion, whichever symbols you need of "<", ">", "=", "not =" and express any values as a fraction e.g. p = 1/3) ?0 =  ?a =  (b) Now suppose Albert makes n = 34 rolls, and a 3 comes up 7 times out of the 34 rolls. Determine the P-value of the test: P-value =

Suppose we want to estimate the average speed of cars traveling on Pacheco Pass, and we want to be able to assert with 98% probability that the average error is at most three miles per hour. How large a sample will we need if it can be shown that o = 7.1 mph? 32 cars O 30 cars 31 cars 29 cars

Explain how I can write or put the 60 and 4 bracket into a scientific calculator and also what does this bracket sign means . thanks

A test was given to a group of students. The grades and gender are summarized below   If one student is chosen at random from those who took the test, find the probability that the student got a 'a 'C'' GIVEN they are male.   Write your answer as a reduced fraction.P(C ∣ male) =   ?

Part I: Probability For each of the following problems, you should write your answer as an expression. Do not give the final numeric value. For example, you should write C(4,2)/24 instead of 0.375. 5. You are playing Scrabble and you draw seven tiles: M, A, T, C, H, E, S. You line them up in some random order on your tile rack (assume all orderings are equally likely). The events M, T, and S are defined as follows: M: The tiles M, A, T, H appear consecutively. T: The tile T appears exactly in the middle (fourth position). S: The tile S is either in the first position or in the final position. Calculate the probability of each event; that is, p(M), p(T), and p(S). 5.1 5.2 What is p(MIT)? 5.3 What is p(MIS)? 5.4 5.5 What is p(T|S)? Consider all pairs of events: (M,T), (M,S), and (T,S). Which pairs of events are independent and which pairs of events are not independent? Justify your answer.

Please see the attached image and answer the green multiple choice poll questions on it.

please show the step by step solution and provide an explanation on why that is the right answer.

Need help with this probability question.

Toilet Flushing In the Healthy Handwashing Survey conducted by Bradley Corporation, it was found that 64%of adult Americans operate the flusher of toilets in public restrooms with their foot. Suppose you survey a random sample of 740 adult American women aged 18–24 years. Use the normal approximation to the binomial to approximate the probability that (a)  exactly 490 of those surveyed flush toilets in public restrooms with their foot.  (b)  no more than 490 of those surveyed flush toilets in public restrooms with their foot.   (c)  at least 503 of those surveyed flush toilets in public restrooms with their foot. What does this result suggest?

According to Reader's Digest,  44% of primary care doctors think their patients receive unnecessary medical care. Use the z-table. a. Suppose a sample of 260 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their patients receive unnecessary medical care. E(p)=  (to 2 decimals)    (to 4 decimals) b. What is the probability that the sample proportion will be within  ±0.03 of the population proportion? Round your answer to four decimals.   c. What is the probability that the sample proportion will be within ±0.05  of the population proportion? Round your answer to four decimals.   d. What would be the effect of taking a larger sample on the probabilities in parts (b) and (c)? Why? The probabilities would - Select your answer -increasedecreaseItem 5 . This is because the increase in the sample size makes the standard error, ,