Reference no: EM132157392

A. If two random samples of sizes 30 and 36 are selected independently from two populations with means 78 and 85, and standard deviations 12 and 15, respectively, then probability that the mean of the 1st sample will be larger than the mean of the 2nd sample is

0.2133

0.0176

0.9823

0.1169

B. In a large university, 20% of the students are business majors. A random sample of 100 students is selected, and their majors are recorded.

1. Compute the standard error of the proportion. 

2. What is the probability that the sample contains at least 12 business majors? 

3. What is the probability that the sample contains less than 15 business majors? 

4. What is the probability that the sample contains between 12 and 14 business majors? 

• 0.044 
• 0.04 
• 0.1056 
• 0.9772

C.    The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours. A simple random sample of 36 bulbs is taken.

1. What is the standard deviation of the sampling distribution? 

2. What is the expected value? 

3. What is the probability that the average life in the sample will be between 2,670.56 and 2,809.76 hours? 

4. What is the probability that the average life in the sample will be greater than 3,219.24 hours? 

5. What is the probability that the average life in the sample will be less than 3,180.96 hours? 

• .9406
• 116
• .0294  
• 3000

D.  The normal distribution can be used to approximate the sampling distribution of the sample proportion with a probability of success 0.8 if the sample size is greater than or equal to ...? (4 decimal places)

E.  The standard error of the mean for a sample of size 179 is 25. In order to cut the standard error of the mean in half (to 12.5) we must select a sample size of