PLEASE HELP SUPER FAST WORTH ALOT OF POINTS The ages of alligators in a swamp are normally distributed, with a mean of 50 years and a standard deviation of 4. Approximately what percentage of the alligators are between 45 and 55 years old?

78.87%

10.56%

89.44%

67.76%

Question 2(Multiple Choice Worth 3 points)

(05.03 LC)

Wait times at an orthodontist's office are typically 17 minutes, with a standard deviation of 2 minutes. What percentage of people should be seen by the doctor between 11 and 23 minutes for this to be considered a normal distribution?

17%

68%

95%

99.7%

1) 78.87%

2) 99.7%

Step-by-step explanation:

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

1- The given data is:

σ = 4 years

μ = 50 years

For X = 45 and X =55

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:

78.87% of alligators.

2- The given data is:

σ = 2 minutes

μ = 17 minutes

For X = 11 and X =23

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:

99.7% of people.

nlgqer

step-by-step