Assuming that the sample mean carapace length is greater than 3.39 inches, what is the probability that the sample mean carapace length is m

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Assuming that the sample mean carapace length is greater than 3.39 inches, what is the probability that the sample mean carapace length is more than 4.03 inches

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  1. Answer:

    The answer is “”.

    Step-by-step explanation:

    Please find the complete question in the attached file.

    We select a sample size n from the confidence interval with the mean [tex]\mu[/tex]and default [tex]\sigma[/tex], then the mean take seriously given as the straight line with a z score given by the confidence interval

    [tex]\mu=3.87\\\\\sigma=2.01\\\\n=110\\\\[/tex]

    Using formula:

    [tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]  

    The probability that perhaps the mean shells length of the sample is over 4.03 pounds is

    [tex]P(X>4.03)=P(z>\frac{4.03-3.87}{\frac{2.01}{\sqrt{110}}})=P(z>0.8349)[/tex]

    Now, we utilize z to get the likelihood, and we use the Excel function for a more exact distribution

    [tex]=\textup{NORM.S.DIST(0.8349,TRUE)}\\\\P(z<0.8349)=0.7981[/tex]

    the required probability:
    [tex]P(z>0.8349)=1-P(z<0.8349)=1-0.7981=\boldsymbol{0.2019}[/tex]

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