Statistics and Probability Answers

How many times do you need to toss a fair coin to get 100 heads with probability 90%?

Roll a dice n times and let X be the number of times you roll 6. Assume that n is large.

(a) Compute the expectation E[X].

(b) Write down an approximation, in terms on n and , of the probability that X diers from its

expectation by less than 10%.

(c) How large should n be so that the probability in (b) is larger than 0.99?

In a survey of 280 adults over 50, 75% said they were taking vitamin supplements. Find the margin of error for this survey if we want a 99% confidence in our estimate of the percent of adults over 50 who take vitamin supplements.

In a survey of 3300 T.V. viewers, 20% said they watch the network news programs. Find the margin of error for this survey if we want a 95% confidence in our estimate of the percent of T.V. viewers who watch network news programs.

Toss a fair coin twice. You win Ghc 1 if at least one of the two tosses comes out heads.

(a) Assume that you play this game 300 times. What is, approximately, the probability that you win

at least Ghc 250?

(b) Approximately how many times do you need to play so that you win at least Ghc 250 with

probability at least 0.99?

Two groups were randomly assigned to spend 15 minutes either in a hot room (defined as 30 degrees Celsius) or a cold room (defined as 0 degrees Celsius). After the 15 minutes elapsed, a mood measure was completed by participants. Scores on the measure of mood ranged from 1-20, with higher scores indicating a better mood. Using an alpha of 0.05, test for a difference between the groups. Group 1 (hot) Group 2 (cold) 13 8 12 8 12 5 9 3 8 3 8 2 a) Which type of test will you use?

What is the probability that 9 package recipients are unemployed

Scott is juggling multiple assignments for his studies. Currently, he has 4 assignments from 4 different subjects (maths, physics, economics, and history) that he needs to start (and complete). He estimates the number of hours taken to complete each of these assignments follow Exponential distributions.

If the time spent on the individual assignment are independent across different subjects, what is the distribution of the total number of hours he expects to spend on all 4 assignments?

 The dean of a particular college is wanting to find out the proportion of students who are interested to enroll in online classes. He made a pre-survey and learned that a proportion of 30% were for the program. How many students will he interview if he is 90% confident and that he considers a margin of error of 4% in conducting the study?

A salesperson for a medical device company has two appointments on a given day. At the first appointment, he believes that he has a 70% chance to make the deal, from which he can earn $1000 commission if successful. On the other hand, he thinks he only has a 40% chance to make the deal at the second appointment, from which, if successful, he can make $1500. What is his expected commission based on his own probability belief? Assume that the appointment results are independent of each other. 

Ministry of Education put a guideline that maximum of 30% students 

are allowed to be in campus to control the spread of Covid-19. In average, 13 students 

will come to Statistics class with standard deviation of 3 students. A sample of 20 

students are chosen. Find probability that the average number of students come to 

Statistics class is at least 18?