Statistics and Probability Answers

A positive z-score always corresponds to an X value greater than the mean. True or False?

Comparing the survey results of votes to the actual votes received by a candidate 

in an election. Identify if it is two tailed or one tailed

A certain area of the eastern United States is, on average, hit by 6 hurricanes a year. Find the prob-ability that in a given year that area will be hit by (a) fewer than 4 hurricanes; (b) anywhere from 6 to 8 hurricanes.

The average height of students in a freshman class of a certain school has been 149.45 cm with a population standard deviation of 7.74 cm. Is there a reason to believe that there has been a change in the average height if a random sample of 43 students in the present freshman class has an average height of 164 cm? Use a 0.01 level of significance.

Write the six steps in hypothesis testing in each of the following studies. Take note, the p-value is already given.

The average family size in the Philippines was reported as 4.25. A random sample of families in a particular street resulted in the following family sizes:

5, 6, 7, 4, 3, 8, 2 and 9

\At 0.10, is the average family size more than the national average?

(p-value = 0.0961)

Suppose in a dice game, the person who rolls two dice wins if his rolls results in a pair of numbers whose sum is 7 or 11. in how many ways can he or she win?

A normally distributed population has a mean of 1,214 and a standard deviation of 122. Find the probability that a single randomly selected element X of the population is between 1,100 and 1,300.

Determine the given and compute the appropriate test statistic of the problem below.

Construct the rejection region of the problem below

In a study of television viewing, the mean number of television program they watched during daytime was 7. A survey was conducted on the random sample of 25 households and found that the mean number of television program they watched during daytime was 5 with a standard deviation of 1.5. Test the hypothesis at 10% level of significance.

Parameter, null hypothesis in symbol, alternative hypothesis in symbol, directional or non directional, level of significance,.

1. A company which produces batteries claims that the life expectancy of their batteries is 90 hours. In order to test the claim, a consumer interest group tested a random sample of 40 batteries. The test resulted to a mean life expectancy of 87 hours. Using a 0.05 level of significance, can it be concluded that the life expectancy of their batteries is less than 90 hours? Assume that the population standard deviation is known to be 10 hours.

A bank Manager wishes to provide a prompt service to customers at the bank derive up windows. The bank currently can serve up to 10 customers per 15 minutes period without significant delay. The average arrival rate is 7 customers per 15 minutes period. Let 𝑥 be the number of customers arriving per 15 minutes period. Assuming that 𝑥 has a Poisson distribution. a) Find

i. The probability that 10 customers will arrive in a particular 15 minutes period. ii. The probability that 10 or fewer customers will arrive in a particular 15 minutes period.

b) Find the probability that there will be a significantly delay at the derive up window. That is to find the probability that more than 10 customers will arrive during a particular 15 minutes period.