When a mean is 40 and standard dev. is 7.5, how do you find probability that a given value will be greater than 55.75?

Question

Abigail Allen · Accepted Answer

#P_(x>55.75)=0.0179#

Given -

Mean #mu =40 #
SD #sigma=7.5#

At #x=55.75#

#z=(x-mu)/sigma=(55.75-40)/7.5=15.75/7.5=2.1#

Probability that a given value will be greater than 55.75 = [Area between z=0 and z=#oo#] - [Area between z= 0 and z=2.1]

#P_(x>55.75)=0.5-0.4821=0.0179#
#P_(x>55.75)=0.0179#

Jameson Allen · Answer

undefined To find the probability that a given value will be greater than 55.75, you would first calculate the z-score using the formula $ z = \frac{x - \mu}{\sigma} $, where $ x $ is the given value, $ \mu $ is the mean, and $ \sigma $ is the standard deviation. Then, you would use a standard normal distribution table or a calculator to find the probability corresponding to that z-score.

Nathan Axel · Answer

undefined To find the probability that a given value will be greater than $ 55.75 $ in a normal distribution with a mean of $ 40 $ and a standard deviation of $ 7.5 $, you can use the z-score formula and then look up the corresponding area under the standard normal curve.

The z-score formula is:

$$ z = \frac{x - \mu}{\sigma} $$

Where:
- $ x $ is the given value ($ 55.75 $ in this case)
- $ \mu $ is the mean ($ 40 $)
- $ \sigma $ is the standard deviation ($ 7.5 $)

Calculate the z-score:

$$ z = \frac{55.75 - 40}{7.5} $$
$$ z = \frac{15.75}{7.5} $$
$$ z = 2.1 $$

Now, you can look up the probability corresponding to a z-score of $ 2.1 $ in a standard normal distribution table or using a calculator. The probability of a z-score greater than $ 2.1 $ is the same as the probability of a value greater than $ 55.75 $ in the original distribution.

From the standard normal distribution table or calculator, the probability corresponding to $ z = 2.1 $ is approximately $ 0.0179 $.

So, the probability that a given value will be greater than $ 55.75 $ is approximately $ 0.0179 $, or $ 1.79\% $.

Avery Alexander · Answer

undefined To find the probability that a given value will be greater than 55.75, you can use the z-score formula and the standard normal distribution table.

First, calculate the z-score of 55.75 using the formula:

$$ z = \frac{x - \mu}{\sigma} $$

where $ x $ is the given value (55.75), $ \mu $ is the mean (40), and $ \sigma $ is the standard deviation (7.5).

$$ z = \frac{55.75 - 40}{7.5} $$
$$ z = \frac{15.75}{7.5} $$
$$ z \approx 2.1 $$

Next, use the standard normal distribution table or a calculator to find the probability associated with a z-score of approximately 2.1. This represents the probability that a value randomly selected from the distribution will be greater than 55.75.

From the standard normal distribution table, the probability corresponding to a z-score of 2.1 is approximately 0.0179.

So, the probability that a given value will be greater than 55.75 is approximately 0.0179, or 1.79%.