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Marta_Voda [28]
2 years ago
8

The average lifetime of a set of tires is 3.4 years. The manufacturer will replace any set of tires failing within three years o

f the date of purchase. The lifetime of these tires is known to follow an exponential distribution. What is the probability that the tires will fail within three years of the date of purchase?
Mathematics
1 answer:
ICE Princess25 [194]2 years ago
7 0

Answer: the probability that the tires will fail within three years of the date of purchase is 0.12

Step-by-step explanation:

The average lifetime of a set of tires is 3.4 years. It means that μ = 3.4

Decay parameter, m = 1/3.4 = 0.294

The probability density function is

f(x) = me^-mx

Where x is a continuous random variable representing the time interval of interest(the reliability period that we are testing)

Since x = 3 years,

Therefore, the probability that the tires will fail within three years of the date of purchase is

f(3) = 0.294e^-(0.294 × 3)

f(3) = 0.294e^- 0.882

f(3) = 0.12

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Answer:

 At the 5% level, BAOI can infer that the average time to complete does not exceeds 60 hours.

Step-by-step explanation:

From the question we are told that

   The  population mean is \mu  =  60 \ hr

    The sample size is  n  =  16

    The  sample mean is  \= x  =  68 \ hr

     The  standard deviation is  \sigma  =  20 \ hr

The  null hypothesis is  H_o  :  \mu  =  60

The  alternative H_a :  \mu >  60

Here we would assume the level of significance of this test to be  

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Next we will obtain the critical value of the level of significance from the normal distribution table, the value is    Z_{0.05} =  1.645

  Generally the test statistics  is mathematically represented as

           t =  \frac{ \= x  - \mu}{  \frac{ \sigma }{\sqrt{n} } }

substituting values

           t =  \frac{  68  - 60 }{  \frac{ 20 }{\sqrt{16} } }

          t = 1.6

Looking at the value of t and  Z_{\alpha } we see that t< Z_{\alpha } hence we fail to reject the null hypothesis

   This means that there no sufficient evidence to conclude that it takes more than 60 hours to complete the course

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   At the 5% level, BAOI can infer that the average time to complete does not exceeds 60 hours.

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1 year ago
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<em>It is important to know that the explanatory variable is the variable that is manipulated by the researcher. </em>

The facts that are not being manipulated are the income of the children studied, and what happens after attending or not preschool program. The variable the researcher is manipulating is the assignation to groups that will or will not attend preschool. Therefore the correct answer is:

(C) Whether or not a subject attends preschool

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