To determine if it is unusual for an individual apartment to have a rent greater than $2781, we will use the normal distribution properties of the rent values. You provided the following key details:

• The mean monthly rent for a one-bedroom apartment in Manhattan is $2643.
• The standard deviation is $502.
• We need to find the probability that a single apartment has a rent greater than $2781.

Steps:

1. Calculate the z-score for $2781 using the formula: $z = \frac{X - \mu}{\sigma}$ where:

   • $X = 2781$ (the rent we're analyzing),
   • $\mu = 2643$ (the mean rent),
   • $\sigma = 502$ (the standard deviation).

2. Once we have the z-score, we can look up the corresponding probability from the standard normal distribution.

Let me compute that for you.The z-score for a rent of $2781 is approximately 0.275.

Next, we will use the standard normal distribution to find the probability that a rent is less than $2781. Then, we can subtract that value from 1 to find the probability of a rent being greater than $2781.

Let me calculate that.The probability that an individual apartment has a rent greater than $2781 is approximately 0.3917, or 39.17%.

Since this probability is relatively high, it would not be considered unusual for an apartment to have a rent greater than $2781.

Do you have any questions or would you like further details on this process?

Here are 5 related questions you might consider:

1. How would the probability change if the rent threshold were higher, say $3000?
2. What is the probability that rent is between $2500 and $3000?
3. How does the probability change if the standard deviation is reduced?
4. What is the significance of a z-score of 1 in this context?
5. How does the sample size affect the probability in such problems?

Tip: Understanding z-scores can help you quickly assess whether a value is unusual or not, based on how far it is from the mean in terms of standard deviations.