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IrinaVladis [17]
4 years ago
8

In a large human population, cranial length is approximately normally distributed with a mean of 185.6 mm and a standard deviati

on of 12.7 mm. What is the probability that a random sample of size 10 from this population will have a mean less than than 180? a. 0.0174 b. 0.1357 c. 0.0823 d. -1.39
Mathematics
1 answer:
iragen [17]4 years ago
8 0

Answer:

The correct option is  c

Step-by-step explanation:

From the question we are told that

   The mean is  \mu = 185.6 \ mm

   The standard deviation is  \sigma = 12.7 \ mm

   The sample size is  n = 10  

    Generally the standard error of the mean is mathematically represented as

      \sigma_{x} = \frac{\sigma}{\sqrt{n} }

=>    \sigma_{x} = \frac{ 12.7}{\sqrt{ 10 } }

=>    \sigma_{x} = 4.016

Generally the probability that a random sample of size 10 from this population will have a mean less than than 180 is mathematically represented as

     P(X <  180 ) = P(\frac{ X - \mu }{\sigma_{x} }  < \frac{180 - 185.6}{4.016} )

\frac{X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ X )

    P(X <  180 ) = P(Z  < - 1.394 )

From the z table  the area under the normal curve to the left corresponding to    -1.394  is  

          P(X <  180 ) = P(Z  < - 1.394 ) = 0.081659

=>      P(X <  180 ) =  0.0823

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Given the function:  f(x) =\frac{x^2}{x^4+16}

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