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Inessa05 [86]
3 years ago
10

A box contains 10 items, of which 3 are defective and 7are non defective. Two items are randomly selected, one at a time, with r

eplacement, and x is the number of defectives in the sample of two. Explain why x is a binomial random variable
Mathematics
1 answer:
lorasvet [3.4K]3 years ago
6 0
Necessary and sufficient conditions for application of binomial distribution :
1. trial must be Bernoulli, i.e. exactly two outcomes (defective or not defective)
2. number of trails is known and not dependent on outcomes (2).
3. probability of each trial must be known and is constant throughout trials (3/10, with replacement)
4. all trials are random and independent of each other.

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A nutrition laboratory tested 25 "reduced sodium" hotdogs of a certain brand, finding that the mean sodium content is 310 mg wit
inessss [21]

Answer:

The  95% confidence interval is  295.9 < \mu< 324.1

A   95% level of confidence mean that there is 95%  chance  that the true population mean will be in this interval

Step-by-step explanation:

From the question we are told that

    The sample size is  n  =  25

    The mean is  \= x  =  310 \ mg

     The standard deviation is  \sigma =  36 \ mg

Given that the confidence level is  95% then the level of significance is mathematically represented as

           \alpha  =  100 - 95

=>        \alpha  =  5\%

=>        \alpha  =  0.05

Next we obtain the critical value of  \frac{\alpha }{2} from the normal distribution table , the value is  

           Z_{\frac{\alpha }{2} } =Z_{\frac{0.05 }{2} }  =  1.96

Generally the margin of error is mathematically represented as

        E =  Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }

substituting values

        E =  1.96 *  \frac{36 }{\sqrt{25} }

        E = 14.1

The 95% level of confidence interval  is mathematically represented as

      \= x - E < \mu

substituting values

     310- 14.1 < \mu< 310+ 14.1

     295.9 < \mu< 324.1

The  95% level of confidence mean that there is 95%  chance  that the true population mean will be in this interval

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Step-by-step explanation:

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Step-by-step explanation:

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Need help on math question thanks <br> A) 0.303 <br> B) 0.435 <br> C) 0.406<br> D) 0.154
Airida [17]

Answer:

A) 0.303

The probability that a randomly selected student from the class has brown eyes , given they are male

P(\frac{B}{M} ) = 0.3030

Step-by-step explanation:

<u>Explanation</u>:-

Given data

                      Brown           Blue           Hazel           Green

Females           13                  4                  6                   9          

Males                10                  2                 9                   12

<em>Let 'B' be the event of brown eyes </em>

<em>Total number of males n(M) = 33</em>

Let B/M be the event of randomly selected student from the class has brown eyes given they are male

<em>The probability that a randomly selected student from the class has brown eyes , given they are male</em>

<em></em>P(\frac{B}{M} ) = \frac{n(B)}{n(M)}<em></em>

<em>From table the brown eyes from males = 10</em>

P(\frac{B}{M} ) = \frac{10}{33}

P(\frac{B}{M} ) = 0.3030

<u>Final answer</u>:-

The probability that a randomly selected student from the class has brown eyes , given they are male

P(\frac{B}{M} ) = 0.3030

8 0
3 years ago
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