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The weights of 1,000 men in a certain town follow a normal distribution with a mean of 150 pounds and a standard deviation of 15 pounds.

From the data, we can conclude that the number of men weighing:

1. More than 165 pounds is _________
2. Less than 135 pounds is about _________

Answer :

Approximately 159 men weigh more than 165 pounds, and approximately 159 men weigh less than 135 pounds.

To determine the number of men weighing more than 165 pounds and less than 135 pounds in a normal distribution, we can use the properties of the standard normal distribution

Given: Mean (") = 150 pounds, Standard Deviation (σ) = 15 pounds

Convert the weights to standard scores (z-scores):

For men weighing more than 165 pounds: z = (165 - 150) / 15 = 1

For men weighing less than 135 pounds: z = (135 - 150) / 15 = -1

Using the z-table, we find the following probabilities:

P(Z > 1) = 0.1587

P(Z < -1) = 0.1587

To find the number of men:

Number of men weighing more than 165 pounds: 0.1587 * 1000 = 159 (approximately)

Number of men weighing less than 135 pounds: 0.1587 * 1000 = 159 (approximately)

Therefore, approximately 159 men will weigh more than 165 pounds, and approximately 159 men will weigh less than 135 pounds.

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Rewritten by : Barada

The number of men weighing more than 165 pounds is approximately 0.1587.

The number of men weighing less than 135 pounds is also approximately 0.1587.

From the given information, we have a normal distribution with a mean of 150 pounds and a standard deviation of 15 pounds. To find the number of men weighing more than 165 pounds or less than 135 pounds, we can use the properties of the standard normal distribution.

Number of men weighing more than 165 pounds:

To find this probability, we need to calculate the area under the normal distribution curve to the right of 165 pounds. We can standardize the value using the formula z = (x - mean) / standard deviation.

z = (165 - 150) / 15

z = 1

Using a standard normal distribution table or a calculator, we can find the probability associated with z = 1. The probability of finding a z-score greater than 1 is approximately 0.1587.

Number of men weighing less than 135 pounds:

Similarly, to find this probability, we need to calculate the area under the normal distribution curve to the left of 135 pounds. We standardize the value:

z = (135 - 150) / 15

z = -1

Using the standard normal distribution table or a calculator, the probability of finding a z-score less than -1 is approximately 0.1587.

for such more question on normal distribution

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