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(50 POINTS) The weights of Rhesus monkeys at the zoo are normally distributed with a mean of 7700 grams and a standard deviation of 250 grams.

What percent of the Rhesus monkeys weigh less than 7200 grams?
A: 0.15%
B: 2.5%
C: 13.5%
D: 16%

User Boileau
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1 Answer

3 votes

The answer is **C: 13.5%**.

To calculate the percentage of Rhesus monkeys that weigh less than 7200 grams, we can use the standard normal distribution. The standard normal distribution is a bell-shaped curve with a mean of 0 and a standard deviation of 1. We can use a z-table to find the probability that a standard normal variable is less than a certain value.

To calculate the z-score of a Rhesus monkey's weight, we can use the following formula:

```

z = (x - μ) / σ

```

where:

* x is the Rhesus monkey's weight

* μ is the mean weight of the Rhesus monkeys (7700 grams)

* σ is the standard deviation of the Rhesus monkeys' weights (250 grams)

For a Rhesus monkey that weighs 7200 grams, the z-score would be:

```

z = (7200 - 7700) / 250 = -2

```

We can then use a z-table to find the probability that a standard normal variable is less than -2. This probability is approximately 0.135.

Therefore, the percentage of Rhesus monkeys that weigh less than 7200 grams is approximately 13.5%

```

13.5

```

User Adriano Mello
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