The mean of a population is 75 and the standard deviation is 14.
The shape of the population is unknown. Determine the probability
of each of the following occurring from this population.
a. A random sample of size 33 yielding a sample mean of 79 or
more
b. A random sample of size 140 yielding a sample mean of between 73
and 77
c. A random sample of size 218 yielding a sample mean of less than
75.7
(Round all the values of z to 2 decimal places and final answers to 4 decimal places.)
Solution :
Given that,
mean = = 75
standard deviation = = 14
a )n = 33
= 75
= / n = 14 33 = 2.4371
a ) P ( >79 )
= 1 - P ( < 79)
= 1 - P ( - /) < (79 - 75 / 2.437 )
= 1 - P( z < 4 / 2.437 )
= 1 - P ( z < 1.64 )
Using z table
= 1 - 0.9495
= 0.0505
Probability = 0.0505
b ) n = 140
= 75
= / n = 14 140 = 1.1832
d ) P (n 73 < < 77 )
P (n 73 - 75 / 1.1832) < ( - / ) < ( 77 - 75 / 1.1832)
P ( - 2./ 1.1832 < z < 2 / 1.1832 )
P (-1.69 < z < 1.69)
P ( z < 1.69) - P ( z < -1.69)
Using z table
= 0.9545 - 0.0455
= 0.9090
Probability = 0.9090
c ) n = 218
= 75
= / n = 14218 =0.9482
P ( < 75.7 )
P ( - /) < (75.7 - 75 / 0.9482)
P ( z < 0.7/ 0.9482)
P ( z < 0.74 )
Using z table
= 0.7704
Probability = 0.7704
The mean of a population is 75 and the standard deviation is 14. The shape of...
A normal population has a mean of 75 and a standard deviation of 5. You select a sample of 40. Use Appendix B1 for the z values Compute the probability that the sample mean is: (Round the zvalues to 2 decimal places and the final answers to 4 decimal places.) a. Less than 74 Probability 09 b. Between 74 and 76. Probability c. Between 76 and 77 Probability d. Greater than 77 Probability Not > 3 of 4 < Prey...
A normal population has a mean of 62 and a standard deviation of 14. You select a random sample of 9. Compute the probability the sample mean is: (Round z values to 2 decimal places and final answers to 4 decimal places.) (a) Greater than 64. Probability (b) Less than 58. Probability (c) Between 58 and 64. Probability
A normal population has a mean of 64 and a standard deviation of 24. You select a random sample of 32. Use Appendix B.1 for the z-values. Compute the probability that the sample mean is: (Round the final answers to 4 decimal places.) a. Greater than 67. Probability b. Less than 60. Probability c. Between 60 and 67. Probability
A population of values has a normal distribution with mean=155.9 and standard deviation=42.1. You intend to draw a random sample of size=12. Find the probability that a single randomly selected value is less than 172.9. P(X<172.9). Find the probability that a sample of size=12 is randomly selected with a mean less than 172.9. P(M<172.9). Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
A normally distributed population has a mean of 475 and a standard deviation of 48. a. Determine the probability that a random sample of size 9 selected from this population will have a sample mean less than 451. b. Determine the probability that a random sample of size 16 selected from the population will have a sample mean greater than or equal to 498. a. P(X<451) = (Round to four decimal places as needed.) b. P(X2498) = 1 (Round to...
A normal population has a mean of 57 and a standard deviation of 14. You select a random sample of 16. Round to 4 decimal places. a. 33% of the time, the sample average will be less than what specific value? Value b. 33% of the time, the value of a randomly selected observation will be less than h. Find h. h c. The probability that the sample average is more than k is 22%. Find k.
A population has a mean of 98.1 and a standard deviation of 27.4. Assuming , the probability, rounded to four decimal places, that the sample mean of a sample of size 77 elements selected from this population will be between 91 and 97 is:
Check my ork A normal population has a mean of 58 and a standard deviation of 13. You select a random sample of 25. Compute the probability that the sample mean Is: (Round your z values to 2 declmal places and final answers to 4 deeclmal places): 12 polnts a. Greater than 60. eBook Ask Print References b. Less than 57 Probability Ask Print References c. Between 57 and 60. Probability Mc
The life expectancy in the United States is 75 with a standard deviation of 7 years. A random sample of 49 individuals is selected. Round all probabilities to four decimal places. What is the probability that the sample mean will be larger than 77 years? Answer What is the probability that the sample mean will be within 1 year of the population mean? What is the probability that the sample mean will be within 2.5 years of the population mean?
Question 5 2 pts An unknown distribution has a mean of 75 and a standard deviation of 18. Samples of size n-30 are drawn randomly from the population. Find the probability that the sample mean is between 80 and 85. (round to 4 decimal places) Example page 397 Wk6Hw_Smp Mean3