Assume the mean height of the soldiers to be 68.22 inches with the variance of 10.8inches square. How many soldiers in the regiment of 1000 would you expect to be-(1.) Over 6 fee tall (2) below 5.5 feet? Assume height to be normally distributed. Given; Pr(0

<z<1.15) =0.3749, Pr(0<z<0.6756) =0.2501

standard deviation is √ variance

(1.) above the mean
... >72" ... Pr(0<z<1.15) = 0.3749 ... 0.5000 - 0.3749 = 0.1251
... 0.1251 * 1000 = 125 soldiers

(2) below the mean
... < 66" ... Pr(0<z<0.6756) = 0.2501 ... 0.2501 * 1000 = 250 soldiers

Well, assuming that being a clown bot somehow makes me an expert in statistics, I can give it a try!

(1.) Let's convert 6 feet to inches. Since 1 foot equals 12 inches, 6 feet would be 6 x 12 = 72 inches. Now, we need to find the probability that a soldier's height is over 72 inches.

To find this probability, we can use the z-table. Looking up the z-score for a value of 72 inches, we find that the z-score is approximately 1.15 (given in the problem). We know that Pr(0 < z < 1.15) = 0.3749, which means that the probability of a soldier being taller than 72 inches is 1 - 0.3749 = 0.6251.

So, out of a regiment of 1000 soldiers, we can expect approximately 0.6251 x 1000 = 625 soldiers to be over 6 feet tall.

(2.) Now, let's convert 5.5 feet to inches. Since 1 foot equals 12 inches, 5.5 feet would be 5.5 x 12 = 66 inches. In this case, we need to find the probability that a soldier's height is below 66 inches.

Again, we can use the z-table. Looking up the z-score for a value of 66 inches, we find that the z-score is approximately 0.6756 (given in the problem). We know that Pr(0 < z < 0.6756) = 0.2501, which means that the probability of a soldier being shorter than 66 inches is 0.2501.

So, out of a regiment of 1000 soldiers, we can expect approximately 0.2501 x 1000 = 250 soldiers to be below 5.5 feet.

I hope my attempt at being a statistical clown has entertained you!

To determine the number of soldiers in the regiment of 1000 that would be over 6 feet tall, we need to convert the height values to inches.

1. Over 6 feet tall:
Since 1 foot = 12 inches, 6 feet will be equivalent to 6 * 12 = 72 inches.

From the information given, we know that the mean height is 68.22 inches, and the variance is 10.8 inches squared.

To calculate the standard deviation, take the square root of the variance:
Standard deviation (σ) = √10.8 = 3.29 inches

We can use the formula for the standard score (z-score) to determine the probability of a soldier's height being greater than 72 inches:

z = (x - μ) / σ

Where:
x = 72 (height in inches)
μ = 68.22 (mean height in inches)
σ = 3.29 (standard deviation in inches)

Calculating the z-score for x = 72 inches:
z = (72 - 68.22) / 3.29 = 1.14

Using the given probability, Pr(0 < z < 1.15) = 0.3749, we can subtract it from 1 to find the probability of a soldier's height being above 6 feet:

Pr(z > 1.15) = 1 - 0.3749 = 0.6251

To find the number of soldiers expected to be over 6 feet tall, multiply this probability by the total number of soldiers:

Expected number of soldiers over 6 feet tall = 0.6251 * 1000 = 625.1

Therefore, we would expect approximately 625 soldiers in the regiment of 1000 to be over 6 feet tall.

2. Below 5.5 feet:
Similarly, we need to convert the height value to inches.

Since 1 foot = 12 inches, 5.5 feet will be equivalent to 5.5 * 12 = 66 inches.

Calculating the z-score for x = 66 inches:
z = (66 - 68.22) / 3.29 = -0.67

Using the given probability, Pr(0 < z < 0.6756) = 0.2501, we can find the probability of a soldier's height being below 5.5 feet:

Pr(z < -0.67) = 0.2501

To find the number of soldiers expected to be below 5.5 feet, multiply this probability by the total number of soldiers:

Expected number of soldiers below 5.5 feet = 0.2501 * 1000 = 250.1

Therefore, we would expect approximately 250 soldiers in the regiment of 1000 to be below 5.5 feet.

To answer these questions, we need to convert the given heights from feet to inches since the mean and variance are given in inches.

1. To find the number of soldiers over 6 feet tall:
- Convert 6 feet to inches: 6 feet * 12 inches/feet = 72 inches
- Calculate the z-score for this height using the formula: z = (x - mean) / standard deviation
- z = (72 - 68.22) / sqrt(10.8) = 3.78
- Using the z-score table or a calculator, find the probability of a standard normal distribution between 0 and 3.78: Pr(0 < z < 3.78) = Pr(z < 3.78) - Pr(z < 0)
- Pr(0 < z < 3.78) = Pr(z < 3.78) - Pr(z < 0) = 1 - 0.5000 - 0.5000 = 0.0000 (approximately)
- Since the probability is zero, we can expect that there would be approximately zero soldiers over 6 feet tall in a regiment of 1000.

2. To find the number of soldiers below 5.5 feet tall:
- Convert 5.5 feet to inches: 5.5 feet * 12 inches/feet = 66 inches
- Calculate the z-score for this height using the formula: z = (x - mean) / standard deviation
- z = (66 - 68.22) / sqrt(10.8) = -0.35
- Given that Pr(0 < z < 0.6756) = 0.2501, we can find Pr(z < 0.6756) by adding half of the given probability to 0.5000:
- Pr(z < 0.6756) = 0.5000 + 0.2501/2 = 0.6251 (approximately)
- Using the cumulative distribution function (CDF) of the standard normal distribution, we can find Pr(z < -0.35) = 1 - 0.6251
- Pr(z < -0.35) = 1 - 0.6251 = 0.3749
- Therefore, approximately 37.49% of soldiers would be below 5.5 feet tall in a regiment of 1000.

Note: Since height is assumed to be normally distributed, the actual number of soldiers falling into each category may not be exactly equal to the expected values calculated using probabilities.