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The lifespans of crocodiles have an approximately Normal distribution, with a mean of 18 years and a standard deviation of 2.6 years. What proportion of crocodiles live between 17.5 and 20.5 years?


Find the z-table here.

0.3147
0.4068
0.5932
0.6853

PLEASE NEED HELP The lifespans of crocodiles have an approximately Normal distribution with a mean of 18 years and a standard deviation of 26 years What proport class=

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Using the normal distribution, it is found that 0.4068 of crocodiles live between 17.5 and 20.5 years.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given as follows:

[tex]\mu = 18, \sigma = 2.6[/tex]

The proportion of crocodiles live between 17.5 and 20.5 years is the p-value of Z when X = 20.5 subtracted by the p-value of Z when X = 17.5, hence:

X = 20.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{20.5 - 18}{2.6}[/tex]

Z = 0.96

Z = 0.96 has a p-value of 0.8315.

X = 17.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{17.5 - 18}{2.6}[/tex]

Z = -0.19

Z = -0.19 has a p-value of 0.4247.

0.8315 - 0.4247 = 0.4068

0.4068 of crocodiles live between 17.5 and 20.5 years.

More can be learned about the normal distribution at  https://brainly.com/question/4079902

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