Complete the following question by hand. The life expectancy in Canada is 77 yea
ID: 3365850 • Letter: C
Question
Complete the following question by hand.
The life expectancy in Canada is 77 years with a standard deviation of 11 years. A random sample of 100 individuals is taken.
In blank #1 enter the mean of the sample means.
In blank #2 enter the standard deviation of the sample means. (Round your answer to 1 decimal places and enter your answer as 0.1 not .1.)
Is the distribution of the sample means normal? Enter "yes" or "no" in blank #3.
In blank #4 enter the probability that the sample mean is less than 75.7 years. (Round your answer to 4 decimal places and enter your answer as 0.1234 not .1234.)
In blank #5 enter the probability that the sample mean is greater than 78.6 years. (Round your answer to 4 decimal places and enter your answer as 0.1234 not .1234.)
In blank #6 enter the probability that the sample mean is between 76 and 77.8 years. (Round your answer to 4 decimal places and enter your answer as 0.1234 not .1234.)
Explanation / Answer
Mean 77.00 Std Dev 11.00 Sample 100.00 Answer 1 Population Mean is same as mean of sample means. 77 Answer 2 Sample Means Standard deviation is Std Dev of population/ square root of sample size 1.1 Answer 3 Yes. Distribution is normal. Because the sample size is large enough to consider the distribution to be normal. Answer 4 Probability for less than 75.7 Z=(75.7-Mean)/Standard deviation of sample -1.1818 Probability for this value from z table is 0.38136 But it is from mean to lower side. So we need to subtract it from 50% to get the region lower than 75.7 0.118640 Answer 5 Probability for greater than 78.6 Z=(78.6-Mean)/Standard deviation of sample 1.4545 Probability for this value from z table is 0.42713 But it is from mean to higher side. So we need to subtract it from 50% to get the region greater than 78.6 0.072870 Answer 6 Probability that the age is in between 76 and 77.8 Calculate 2 Z values and add probability for each Z=(76-Mean)/Standard deviation of sample -0.90909091 Probability for this value from z table is 0.31833 Z=(77.8-Mean)/Standard deviation of sample 0.727272727 Probability for this value from z table is 0.266432 Adding both probabilities gives the percentage of population between 76 and 77.8 0.584762