Question

For the red blood cell (RBC) count in females, with a mean of 4.8 million per cubic millimeter of whole blood and a standard deviation σ = 0.3 (based on information from Diagnostic Tests with Nursing Implications, edited by S. Loeb, Springhouse Press). Convert each of the following x intervals to z intervals.

(a) 4.5(b) x<4.2
(c) 4.0
For the interval 4.5a) z<−1
b) z>1
c) −1d) z=0

For the interval x<4.2, the corresponding z interval is:
a) z<−2
b) z>2
c) z<−1
d) z=0

For the interval 4.0a) −1b) z<−1
c) z>2
d) z=0

Answer 1

The x intervals given are converted to z intervals by subtracting the mean and dividing by the standard deviation. For an RBC count with mean 4.8 million/mm³ and standard deviation 0.3, the intervals 4.5, x<4.2, and 4.0 correspond to z = -1, z < -2, and z < -2, respectively.

Step-by-step explanation:

To convert the given x intervals to z intervals for a red blood cell (RBC) count with a mean of 4.8 million per cubic millimeter and a standard deviation σ = 0.3, we use the z-score formula: z = (x - μ) / σ, where x is the value in the x interval, μ is the mean, and σ is the standard deviation.

• For x = 4.5: z = (4.5 - 4.8) / 0.3 = -1
• For x < 4.2: z < (4.2 - 4.8) / 0.3 = -2
• For x = 4.0: z = (4.0 - 4.8) / 0.3 = -2.67, which is less than -2

Therefore, the corresponding z intervals are:

• For the interval 4.5: z = -1
• For the interval x < 4.2: z < -2
• For the interval 4.0: z < -2 (as it is less than -2)