Normal Distribution (2 decimal) 1. A study finds that the carapace length of an

Question

Normal Distribution (2 decimal)

1. A study finds that the carapace length of an adult spider is normally distributed with a mean of 15.81 mm and a standard deviation of 1.69mm. Let x denote carapace length for the adult spide. Sketch the distribution of the a, variable, x, including z-value 1,2,3 standard deviation above and below the mean.

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2. Assume that the variable under consideration has a density curve. The area under the density curve that lies to the right of 11 is 0.424.

a. What percentage of all possible observations of the variable exceed 11?

b. What percentage of all possible observations of the variable are at most 11?

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3. Use a standard normal table to obtain the areas under the normal curve described below. Sketch a standard normal curve and shade the area of interest.

a. The area either to the left of -1.54 or to the right of 1.19.

b. The area either to the left of 0.59 or to the right of 1.67.

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4. Assume that the variable under consideration has a density curve. It is given that 29.6% of all possible observations of the variable are less that 19. a. Determine the area under the density curve that lies to the left of 19. b. Determine the area under the density curve that lies to the right of 19.

Explanation / Answer

Ans:

2)Given that

P(x>11)=0.424

a)percentage of all possible observations of the variable exceed 11=0.424

b)percentage of all possible observations of the variable are at most 11=1-0.424=0.576

3)

a)P(z<-1.54)+P(z>1.19)=0.0618+0.1170=0.1788

b)P(z<0.59)+P(z>1.67)=0.7224+0.0475=0.7699

4)Given that

P(x<19)=0.296

a)Area that lies to the left of 19=0.296

b)Area that lies to the right of 19=1-0.296=0.704

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