Statistics and Probability Answers

in a math test,the mean is 45,and the standard deviation is 4.Assuming normality,what is the probability that a score picked at random will lie above score is 50

The average height of students in a freshman class of a certain school has been 161.27 cm with a population standard deviation of 6.5 cm. Is there a reason to believe that there has been a change in the average height if a random sample of 45 students in the present freshman class has an average height of 150.6 cm? Use a 0.05 level of significance.

Let X be a random variable with the following probability distribution:

x. -3 , 6 , 9

P(X=x). 1/6 , 1/2 , 1/3

Find ug(x), where g(X)= (2X+1)^2

Chinovac Labs tried a new vaccine on 165 randomly selected individuals. From the experiment, it was determined that 82 of them developed immunity. Calculate a 95% confidence interval for the proportion p of individuals in the population for whom the vaccine would help. What is the lower bound of this interval?

11. Q10. Assume your run the statistics to test the hypothesis and your result is 0.06, and then what will be your decision as a researcher, at P is 5%?

Chinovac Labs tried a new vaccine on 189 randomly selected individuals. From the experiment, it was determined that 104 of them developed immunity. Calculate a 95% confidence interval for the proportion p of individuals in the population for whom the vaccine would help. What is the upper bound of this interval?

6 % of the 100 students in Emmie Xi Hem International School students said that they had been late in their first-period classes. What is the upper bound of the 99% confidence interval for the proportion of students in the said school who had been late in their first-period classes?

Chinovac Labs tried a new vaccine on 126 randomly selected individuals. From the experiment, it was determined that 118 of them developed immunity. Calculate a 95% confidence interval for the proportion p of individuals in the population for whom the vaccine would help. What is the point estimate of this interval?

The Malayo Colleges Mindanao recently conducted a study analyzing the privacy management habits of teen internet users. In a group of 116 teens, 80 reported having more than 100 followers on Twitter. Find the upper bound of a 90% confidence interval for the true proportion of teens who would report having more than 100 followers on Twitter. 

A LED company claims that the average life of the LED light bulbs it

manufactures is 1, 500 hours with a standard deviation of 500 hours. If a random

sample of 40 bulbs is chosen, what is the probability that the sample mean will be:

a. greater than 1, 400 hours?

b. less than 1, 400 hours?