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Chapter 6: Q. 77 (page 404)

77. Blood types Refer to Exercise 75. How surprising would it be to get more than 4 adults with type O blood in the sample? Calculate an appropriate probability to support your answer.

Short Answer

Expert verified

The probability is greater than 5%, it is not unlikely to obtain more than 4adults with blood type鈼�is P(x>4)=0.1402=14.02%and so the result is not surprising.

Step by step solution

01

Concept introduction

The proportion of the number of outcomes in a total group of similarly probable effects that supply a particular event to the complete number of potential products is known as probability in statistics.

02

Explanation

Given:
n=7
p=0.44
Let's use the Binomial Probability:
P(X=k)=nk脳pk脳(1鈭�p)n鈭�k

P(X=5)=75脳(0.44)5脳(0.66)7鈭�5鈮�0.10861

P(X=6)=76脳(0.44)5脳(0.66)7鈭�6鈮�0.0284

P(X=7)=77脳(0.44)7脳(0.66)7鈭�7鈮�0.00321

P(x>4)=P(x=5)+P(x=6)+P(x=7)=0.0186+0.0284+0.0032=0.1402=14.02%

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Most popular questions from this chapter

85. Aircraft engines Engineers define reliability as the probability that an item will perform its function under specific conditions for a specific period of time. A certain model of aircraft engine is designed so that each engine has probability 0.999 of performing properly for an hour of flight. Company engineers test an SRS of 350 engines of this model. Let X= the number that operate for an hour without failure.
(a) Explain whyX is a binomial random variable.

(b) Find the mean and standard deviation ofX. Interpret each value in context.
(c) Two engines failed the test. Are you convinced that this model of engine is less reliable than it鈥檚 supposed to be? Compute P(X鈮�348) and use the result to justify your answer.

14. . Life insurance A life insurance company sells a term insurance policy to a 21-year-old male that pays \(100,000if the insured dies within the next 5years. The probability that a randomly chosen male will die each year can be found in mortality tables. The company collects a premium of \)250each year a payment for the insurance. The amount Ythat the company earns on this policy is \(250per year, less the \)100,000that it must pay if the insured dies. Here is a partially completed table that shows information about risk of mortality and the values of Y=profit earned by the company:

(a) Copy the table onto your paper. Fill in the missing values of Y.
(b) Find the missing probability. Show your work.
(c) Calculate the mean 渭Y.Interpret this value in context

79. Sowing seeds Refer to Exercise 69.

(a) Find the probability that exactly17 seeds germinate. Show your work.
(b) If only 12seeds actually germinate, should Judy be suspicious that the company鈥檚 claim is not true? Compute P(X鈮�12)and use this result to support your answer.

83. Random digit dialing Refer to Exercise 81. Let Y= the number of calls that don鈥檛 reach a live person.

(a) Find the mean of Y. How is it related to the mean of X? Explain why this makes sense.
(b) Find the standard deviation of Y.How is it related to the standard deviation of X? Explain why this makes sense

Spell-checking Refer to Exercise 3. Calculate and interpret the standard deviation of the random variable X. Show your work
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