Statistics and Probability Answers

Hello, I got a hard problem and I'm not an expert on maths so I would love some help,

I play a game where there are 2 possible outcomes, win or lose. What if the chance of winning is let's say 55%, and I play this game, let's say 500 times, what is the chance of winning more than half of all games(so 250 out of all 500 games)? Or what is the chance of winning more than 52% of the games? Is there a formula for this? I tried looking it up on google but I couldn't find.

Would love if you answer :)

7) The body temperatures of adults are normally distributed with a mean of 98.6 degree F and a standard deviation of 0.60 degree F. If 36 adults are randomly selected, find the probability that their mean body temperature is greater than 98.4 degree F.

The International Air Transport Association survey's business travelers to develop quality rating for transatlantic gateways airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each travelers is ask to provide a rating for the Miami International Airport . The rating obtained from the sample of 50 business travelers follow :


6 4 6 8 7 7 6 3 3 8 10 4 8
7 8 7 5 9 5 8 4 3 8 5 5 4
4 4 8 4 5 6 2 5 9 9 8 4 8
9 9 5 9 7 8 3 10 8 9 6

Develop a 95% confidence interval estimate of the population mean rating for Miami.

A manufacturer is studying the effects of cooking temperature, cooking time, and type of cooking oil for making potato chips. Three different temperatures, 4 different cooking times, and 3 different oils are to be used.
(a) What is the total number of combinations to be studied?
(b) How many combinations will be used for each type of oil?
(c) Discuss why permutations are not an issue in this exercise.

3. A researcher is interested in whether listening to music helps or hinders test-performance. To control for differences in cognitive level, this researcher decides to use a within-participants design. He selects a random sample of participants and has them study different material of equal difficulty in both the music and no music conditions. Participants take a 20-item quiz on the material. The table below shows the scores on the quiz. The study is completely counterbalanced to control for order effects. The scores obtained are measured on an interval-ratio scale and are normally distributed. Music: 17,16,15,16,18,18; no music: 17,18,17,17,19,18. What statistical data should be used to analyze the data? Is this a one- or two-tailed test? Identify Ho and Ha for this study. Conduct the appropriate analysis. Should Ho be rejected? What should the researcher conclude? Calculate the 95 confidence interval.

In one city, 51.5% of adults are female, 8.2% of adults are left-handed, and 5.2% are left-handed females. For an adult selected at random from the let
F = event that person is female
L = event person is left handed.
Find P (F or L) Round approximations the three decimal places.

The heights of 10 year old boys and girls closely follow a normal distribution with the mean of 51 inches and standard deviation of 2 inches.
a. what percentage of 10 year olds are shorter than 50 inches?
b. What percentage of 10 yr olds are between 48 and 54?

the probability that a candidate passes in physics is 70% and that he passes in chemistry is 40%. What is the probability that the candidate passes in any one of the two subjects?

if 16 dates are named at random, What is the probability that 3 of them will be Sundays?

if A and B are two candidates mutually exclusive events and P(AUB) is not equal to 0, then show that P[A/AUB] = P(A)/P(A) + P(B)