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julia-pushkina [17]
2 years ago
9

2. The mean birth weight of a full term boy born in the US is 7.7 lbs, with standard deviation of 1.1 lbs. A. Find the probabili

ty that a boy born full term in the US weighs less than 7 lbs. B. Find the probability that the average weight of 25 baby boys born in a particular hospital have an average weight less than 7 lbs.
Mathematics
1 answer:
Fed [463]2 years ago
4 0

Answer:

A

The value is P( X  <  7 ) =0.26226

B

The value is P( X  <  7 ) = 0.00073

Step-by-step explanation:

From the question we are told that

  The population mean is  \mu = 7.7 lbs

   The standard deviation is \sigma  = 1.1 \ lbs

  The sample size is  n =  25

Generally the probability that a boy born full term in the US weighs less than 7 lbs is mathematically represented as

     P( X  <  7 ) =  P( \frac{X - \mu }{\sigma}  <  \frac{7 - 7.7 }{1.1 } )

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

=>   P( X  <  7 ) =  P(Z

From the z table  the area under the normal curve to the left corresponding to    -0.6364  is

    P(Z

=>   P( X  <  7 ) =0.26226

Generally the standard error of mean is mathematically represented as  

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

=>     \sigma_{x} = \frac{ 1.1  }{\sqrt{25} }

=>     \sigma_{x} = 0.22

Generally the probability that the average weight of 25 baby boys born in a particular hospital have an average weight less than 7 lbs is mathematically represented as

         P( \= X  <  7 ) =  P( \frac{\= X - \mu }{\sigma_{x}}  <  \frac{7 - 7.7 }{ 0.22 } )

=>      P( X  <  7 ) =  P(Z

From the z table  the area under the normal curve to the left corresponding to    -3.1818  is

=>      P(Z

=>      P( X  <  7 ) = 0.00073

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An aptitude test has a mean score of 80 and a standard deviation of 5. The population of scores is normally distributed. What pr
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Answer:

2.28% of tests has scores over 90.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 80, \sigma = 5

What proportion of tests has scores over 90?

This proportion is 1 subtracted by the pvalue of Z when X = 90. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{90 - 80}{5}

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Z = 2 has a pvalue of 0.9772.

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At Hogwarts School of Witchcraft and Wizardry, Professor Snape was concerned about grade inflation, and suggested that the schoo
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Answers:

The z scores are approximately:

  • Care of Magical Creatures:  z = 0.333
  • Defense Against the Dark Arts:  z = 0.583
  • Transfiguration:  z = -0.263
  • Potions: z = -0.533

From those scores, we can say:

  • Best grade = Defense Against the Dark Arts
  • Worst grade = Potions

=====================================================

Further Explanation:

We'll need to convert each given score to a corresponding standardized z score.

The formula to use is

z = (x - mu)/sigma

where,

  • x = given grade for each class
  • mu = mean
  • sigma = standard deviation

Let's find the z score for the Care of Magical Creatures class

z = (x - mu)/sigma

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z = 0.333 approximately

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And for the Transfiguration class as well

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z = (3.10 - 3.20)/(0.38)

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The negative z score means his grade below the average, whereas earlier the other scores were above the average since he got positive z scores.

Now do the final class (Potions) to get this z score

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This grade is below average as well.

----------------------------

To summarize, we have these z scores

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  • Defense Against the Dark Arts:  z = 0.583
  • Transfiguration:  z = -0.263
  • Potions: z = -0.533

Harry did his best in Defense Against the Dark Arts because the z score of 0.583 (approximate) is the largest of the four z scores. On the other hand, his worst grade is in Potions because -0.533 is the lowest z score.

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