Statistics and Probability Answers

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 A coin tossed thrice. Find: 

 a. The probability of getting exactly 3 heads. 

 b. The probability of getting exactly 2 tails.

 c. The probability of getting atmost 1 head. 

 d. The probability of getting atleast 1 tail.

1. P23 

2. P51 

3. P63 

4. P49 

5. P88 

6. P93 

7. P90 

8. P12 

9. P75 

10.P100 

1. Data from the school clinic shows that the average height of grade 11 students is 160 cm with a population standard deviation of 1.5. A sample of 50 students has an average height of 164 cm. Test the hypothesis that the average height is 160 cm.

a) formulate the null and alternative hypothesis

b) Determine what test statistic to use

c) Calculate the test statistic value

A researcher wants to estimate the numbers of hours that 5 years old children spend watching television. A sample of 50 five-year old children was observed to have a mean viewing time of 5 hours. The population is normally distributed with a population standard deviation of 0.5 hours. Find the 95% confidence interval of the population mean.

Given the population 1,3,4,6 and 8. Suppose samples of size 3 are drawn from this population. How many different samples can be drawn from this population?

Customers at the restaurant have to wait an average of 25 minutes before they receive their meal from the time their order was placed. Assume these waiting times are normally distributed with a standard deviation of 5 minutes.

3.1) What is the probability that a randomly selected customer waits between 20 and 35 minutes before receiving his meal from the time his order was placed?

3.2) What is the maximum waiting time for a customer to receive her meal if she is in the 10% of customers who receive their meals in the fastest time from when the order was placed?

The lifetime X of an alkaline battery is exponentially distributed with lambda = 0.05 per hour. What are the mean and standard deviation of the battery’s lifetime

Investigating a complaint from a buyer that there is short-weight selling, a manufacturer takes a random sample of twenty-five 32 g cans of coffee from a large shipment and finds that the mean weight is 31 g with a standard deviation of 0.6 g. Is there evidence of short-weighing at the 0.01 level significance?

Carl has completed 8 math homework assignments that are all worth 20 points, and his mean score is 17.

Carlos has two more 20-point homework assignments to complete before his progress report gets sent

out, and he wants to raise his mean score to an 18. Is it possible for Carlos to raise his mean score to an

18? If it is possible, explain what scores he would need to get, and if not, explain why not.

Random samples of size 4 are drawn with replacement form finite population 3, 6, 9, 20. What is the variance of the sample?