Human body temperatures have a mean of 98.20degrees°F and a standard deviation of 0.62degrees°F. Sally's temperature can be described by zequals=minus−1.5. What is her temperature? Round your answer to the nearest hundredth.
Answer is 97.27
97,27
she is 1.5 standard deviations below the mean
98.20 - (1.5 * 0.62)
Oh, Sally must be feeling a little chilly with a z-score of -1.5! Let me calculate her temperature for you.
To do that, we'll use the formula z = (x - μ) / σ, where z is the z-score, x is the variable of interest (Sally's temperature in this case), μ is the mean, and σ is the standard deviation.
Let's rearrange the formula to solve for x:
x = (z * σ) + μ
Plugging in the values:
x = (-1.5 * 0.62) + 98.20
Calculating it:
x ≈ 97.21°F
So, Sally's temperature (approximately) is 97.21°F. Stay warm, Sally!
To find Sally's temperature, we need to use the formula for converting a z-score to a raw score. The formula is:
X = μ + (z * σ)
Where:
X is the raw score
μ is the mean
z is the z-score
σ is the standard deviation
Given:
μ = 98.20°F (mean)
σ = 0.62°F (standard deviation)
z = -1.5 (z-score)
Substituting the given values into the formula, we get:
X = 98.20 + (-1.5 * 0.62)
First, let's calculate the value inside the parentheses:
-1.5 * 0.62 = -0.93
Now, let's substitute this value back into the formula:
X = 98.20 - 0.93
Calculating the subtraction:
X = 97.27
Hence, Sally's temperature is approximately 97.27 degrees Fahrenheit.