Question

PLEASE HELP SUPER FAST WORTH ALOT OF POINTS

Answer 1

Answer:

1) 78.87%

2) 99.7%

Step-by-step explanation:

The z-score for a normal distribution is given by:

$z=\frac{X-\mu}{\sigma}$

1- The given data is:

σ = 4 years

μ = 50 years

For X = 45 and X =55

$z_1=\frac{45-50}{4}\\z_1=-1.25\\z_2=\frac{55-50}{4}\\z_2=1.25$

A z-score of -1.25 corresponds to the 10.57th percentile of a normal distribution, while a z-score of 1.25 is equivalent to the 89.44th percentile.

Therefore, the percentage of the alligators are between 45 and 55 years old is:

$P=89.44-10.57=78.87\%$

78.87% of alligators.

2- The given data is:

σ = 2 minutes

μ = 17 minutes

For X = 11 and X =23

$z_1=\frac{11-17}{2}\\z_1=-3\\z_2=\frac{23-17}{2}\\z_2=3$

A z-score of -3.0 corresponds to the 0.135th percentile of a normal distribution, while a z-score of 3.0 is equivalent to the 99.865th percentile.

Therefore, the percentage of people that should be seen by the doctor between 11 and 23 minutes is:

$P=99.865-.0135=99.73\%$

99.7% of people.