WILL GIVE BRAINEST For the x-values 1,2,3, and so on, y-values...

The lifespan (in days) of the common housefly is best modeled using a normal curve having mean 22 days and standard deviation 5.

Natasha_Volkova [10]

Answer:

Yes, it would be unusual.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If $Z \leq -2$ or $Z \geq 2$ , the outcome X is considered unusual.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

$\mu = 22, \sigma = 5, n = 25, s = \frac{5}{\sqrt{25}} = 1$

Would it be unusual for this sample mean to be less than 19 days?

We have to find Z when X = 19. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{19 - 22}{1}$

$Z = -3$

$Z = -3 \leq -2$ , so yes, the sample mean being less than 19 days would be considered an unusual outcome.

7 0

2 years ago

Which expressions are equivalent to 7x – 14? Check all that apply. 14 – 7x x – 2 –(14 – 7x) 7(x – 2) 3x – 14 4x 2x – 10 5x 4.

kondaur [170]

Linear equation are the equation which has the highest power of the unknown variable is 1.The expressions given in the option 1, 2, and 3 are equivalent to $7x - 14$ .