Question

PROBLEM 1: Among all the forms of income declaration for payment and taxes, completed in a certain year, the average of the tax paid was $ 2000 and the standard deviation was $ 500. In addition, in 10% of the forms, the tax paid was higher to $ 3000. A random sample of 625 forms of income declaration is taken for the payment of taxes. What is the probability that more than 60 of the sample forms have a tax greater than $ 3000? POSSIBLE ANSWERS: a) 0.3936 b) 0.6460 c) 0.3639 d) 0.6064

PROBLEM 2: The following data is about the bending strength (MPa) of concrete beams of a certain type: 5.3, 5.4, 8.3, 7.4, 7.1, 8.3, 5.7, 6.5, 7.9, 6.9 Calculate the point estimate of the mean resistance value for the conceptual population of all beams fabricated in this way and tell what estimator use. POSSIBLE ANSWERS: a) 6.88, the sample mean b) 7.00, the sample median c) 8.30, sample fashion d) No answer is correct

PROBLEM 3: Among all the income tax return forms, completed in a certain year, the average tax paid was $ 2000 and the standard deviation was $ 500. In addition, in 10% of the forms, the tax paid was higher to $ 3000. A random sample of 625 forms of income declaration is taken for the payment of taxes. What is the probability that the average tax paid on sample forms is greater than $ 1980? POSSIBLE ANSWERS: a) 0.1586 b) 0.8413 c) 0.7890 d) No answer is correct

PROBLEM 4: The bags of a concrete mix, labeled with a weight of 100 pounds, have an average population weight of 100.15 pounds and a population standard deviation of 10 pounds. What is the probability that the average weight of a sample of size 33 is less than 101 pounds? POSSIBLE ANSWERS: a) no answer is correct b) 0.6873 c) 0.3127 d) 0.4656

PROBLEM 5: Juanita Martínez, a researcher at the Colombian Cofee Corporation, is interested in determining the rate of coffee use per household in the United States. She believes that the annual consumption per household has a mean μ = 18 pounds and standard deviation close to 4 pounds. If Juanita takes a sample of 36 households and records her coffee consumption for a year, what is the probability that the average sample is between 14 and 20 pounds? POSSIBLE ANSWERS: a) 0.9986 b) No answer is correct c) 0.9657 d) 0.0014

Answer 1

1)Solution:

n = 625

p = 0.10

binomial probability distribution

Formula:

P_{(k out of n )}= n!*p^k * q^n-k / k! *(n - k)!

P( x > 60 ) = 625!*0.1⁶¹ * 0.9^625-61 / 61! *(625 - 61)!+625!*0.1⁶² * 0.9^625-62 / 62! *(625 - 62)!.......

...........+625!*0.1⁶²⁵ * 0.9^625-625 / 60! *(625 - 625)!

= 0.5987

the near answer is option d