Question

The high temperatures for days in January are Normally distributed with a mean of 38 degrees Fahrenheit and a standard deviation of 5 degrees . How many days in January will have temperatures betleen degrees Fahrenheit and 43 degrees Fahrenheit ? Round your answer to two decimal places .

Answer 1

Answer:

0.6826

Step-by-step explanation:

The high temperatures for days in January are Normally distributed with a mean of 38 degrees Fahrenheit and a standard deviation of 5 degrees . How many days in January will have temperatures between 33 degrees Fahrenheit and 43 degrees Fahrenheit ? Round your answer to two decimal places.

Solution:

The z score is a score used in statistics to determine by how many standard deviations the raw score is above or below the mean. The z score is given by the formula:

$z=\frac{x-\mu}{\sigma} \\\\where\ \mu=mean,s=raw\ score \ and\ \sigma=standard\ deviation\\\\Given\ that\ \mu=38^oF,\sigma=5^oF\\\\For\ x=33^oF\\\\z=\frac{x-\mu}{\sigma}=\frac{33-38}{5}= -1\\\\For\ x=43^oF\\\\z=\frac{x-\mu}{\sigma}=\frac{43-38}{5}= 1$

From the normal distribution table, P(33 < x < 43) = P(-1 < z < 1) = P(z < 1) - P(z < -1) = 0.8413 - 0.1587 = 0.6826