Question

The length of the western rattlesnake is normally distributed with a mean of 42 inches and a standard deviation of 2 inches. Let x denote length for western rattlesnakes. 3. a. Use MATHCAD to draw the distribution of the variable x, then use cut-and-paste to transfer the output of MATHCAD into this document Determine and show the formula for the standardized version, z, of the variable x. Identify and draw the distribution of z. The percentage of western rattlesnakes that have lengths between 35 inches and 40 inches is equal to b. c. d. the area under the standard normal curve between and That percentage is The percentage of western rattlesnakes that have lengths less than 45 inches is equal to the area under the standard normal curve that lies to the e. That percentage is eof

Answer 1

3. X ~ Normal(42, 2²)

a) The plot of the distribution of X is :

Distribution Plot Normal, Mean-42, StDev-2 0.20 0.15 0.05 0.00 35.0 37.5 섹꾜.co 42.5 45.0 47.5

b) The standardized variable is

T-mean 2.-42 standard deviation

c) The plot of the distribution of Z is :

Distribution Plot Normal, Mean 0, StDev-1 0.4 0.3 S 0.2 0.1 2 0 -3 2

d) z value for x = 35 is

35-42 3.5

z value for x = 40 is

40-42

The percentage of western rattlesnakes that have lengths between 35 inches and 40 inches is equal to the area under the standard normal curve between -3.5 and 1

That percentage is

100 * P(-3.5 < Z <-1)

100 * P(Z <-1) _ P(Z <-3.5)

100 * 4) (-1)-Ф(-3.5)|

100 * (0.158655-0.0002326)

1000.158422

$=15.8422\%$

e) z value for x = 45 is

45-42 = 1.5

The percentage of western rattlesnakes that have lengths less than 45 inches is equal to the area under the standard normal curve between $-\infty$ and 1.5.

The percentage is

100* P(X < 45)

$=100* \Phi(1.5)$