1. From a box containing 10 red, 30 white, 20 blue and 15 orangeballs, 5 are drawn at random. Find the probability that:
a) All are white - 0.008256723
b) Be red, white or blue - 0.009169617
c) They are neither red nor blue - 0.070788

2. A company will launch three new shampoos. It is believed thatthe probability that the first one is successful is 0.45, that thesecond one has it is 0.55 and that the third one has it is 0.75.What is the probability that
a) The three succeed? - 0.185625
b) At least two succeed? -
c) None succeed?

3. You have three boxes. In the first there are 6 rabbits and 2pigeons; in the second, 8 rabbits and 5 pigeons, and in the third 4rabbits and 6 pigeons. What is the probability of
a) take out a rabbit?
b) that the rabbit comes from the third box?
4. An exam has 10 multiple-choice questions. There are fourpossible answers for each question. Luis has not studied for theexam and has decided to do it at random. Assuming that you need 70%of the correct questions to pass, calculate the probability thatLuis will pass the exam.

5. On average, four imperfections are observed in each 50mstretch of network cable. Calculate the probability that, in a 25 msection of this type of network cable:
a) More than three imperfections are observed b) At least oneimperfection

6. According to one study, 30% of adults suffer from insomnia.If you find a group of randomly selected adults, what is theprobability that:
a) the sixth revised is the first to suffer insomnia?
b) the fifth review is the third to suffer insomnia?

7. The weight of a newborn baby in a certain country is a randomvariable that follows a normal distribution with an average of 3.2kg. And standard deviation of 0.4 kg.
a) Determine the percentage of newborn babies weighing 3.5 kg ormore - 0.2266
b) Calculate the conditional probability that a newborn baby weighsmore than 3.5 kg, if it is known to weigh at least 3 kg -0.3277
c) From what weight is 10% of babies born weighing more? - 3.7126Kg
   
8. In a hospital, 22% of transplants are cornea. Use theapproximation to the binomial distribution by normal to calculatethe probability that, in the following 120 transplants:
a) 30 are cornea - 0.0641
b) at least 30 are from the cornea - 0.1831

9. In a company of 5000 workers, it is desirable to know if thepositive assessment of management management has varied greatly,which last year was conclusively concluded that it was 80% of theworkers. For this, a sample of size 200 is carried out, resultingin the positive assessment being considered by 55% of the workerssurveyed. Can we affirm that the valuation has varied with theprobability of being 1% wrong? - Yes it has varied

10. A company producing pasteurized milk has as a rule not toaccept raw milk with a fat content exceeding 34 g / 100g. A sampleof 36 liters of milk obtained from as many cows belonging to thesame farm gave an average value of fat content in milk of 35.2 g /100g with a deviation of 4.1 g / 100g. Can milk be accepted by thepasteurizer? The company admits an error level of 1%. - Yes milk isaccepted.
11. Calculate Zα / 2 in the following sections

a) With a confidence level of 96% - 2.05
b) With a confidence level of 99.5% and 92% - 2.81 and 1.75
c) with a level of significance of 2% and 7% - 2.32 and 1.81
d) With α = 0.03 and α = 0.11 - 2.17 and 1.6

12. A factory produces steel cables, whose resilience follows anormal distribution of unknown mean and standard deviation σ = 10KJ / m3. A sample of 100 pieces was taken and through a statisticalstudy a confidence interval (898.04 - 901.96) was obtained for theaverage resilience of the steel cables produced in the factory.

a) Calculate the value of the average resilience of the 100pieces of the sample. - 900
b) Calculate the level of confidence with which this interval hasbeen obtained. - 95% confidence
c) If you would like to have an error of 3 KJ / m3 in theconfidence interval, what size should the sample be? A sampleof

13. It is known that the average electric power consumption in acertain province is 721 Kwh.

A technology company in the region believes that its employeesconsume more than the provincial average. Collect information onthe consumption of 15 randomly chosen employees, and obtain thefollowing data:

710 774 814 768 823
732 675 755 770 660
654 757 736 677 797

If the distribution of monthly electricity consumption isnormal:

a) Is there evidence to state that the average householdelectric power consumption of the company's employees is higherthan the average consumption at the provincial level? Use asignificance level of 10%. - Yes there is evidence.
b) What is the p-value of the decision? - 0.0878

14. An electric company manufactures cell phone batteries thathave a duration that is distributed approximately normally with anaverage of 800 hours and a standard deviation of 40 hours. A randomsample of 30 batteries has an average duration of 785 hours.

a) Do the data show sufficient evidence to say that the averageduration is less than 800? Use a significance level of 5%. - Yesthere is evidence to say that it is minor.
b) What is the probability of deciding that the average is 800hours when in reality it is 780 hours? - 0.1357 (they don't comelike this on the exam, it's difficult and they have to deduceseveral things)

15. A cake factory manufactures, in its usual production, 3% ofdefective cakes. A customer receives an order of 500 cakes from thefactory. Calculate the probability that ...
a) Find more than 5% of defective cakes. - 0.004375
b) Find between 1% and 3% of defective cakes. - 0.4956
c) Calculate a 95% confidence interval for the percentage ofdefective cakes. (0.015-0.4495)

16. It is assumed that the distribution of the temperature ofthe human body in the population has an average of 37ºC and astandard deviation of 0.85ºC. A sample of 105 people is chosen,calculate the following probabilities:
a) That the average is less than or equal to 36.9 ºC - 0.114
b) That the average is greater than 38.5 ºC - 0
c) Find from what temperature 10% of the hottest bodies are found.- 38.09
d) Find from what temperature 5% of the coldest bodies are found. -35.6