Questions: The Standard Normal Distribution (μ=0, σ=1) (a) Convert the x interval, 4.5<x, to a z interval. <z (b) Convert the x interval, x<4.2, to a z interval. z< (c) Convert the x interval, 4.0<x<5.5, to a z interval. <z< (d) Convert the z interval, z<-1.44, to an x interval. (Round your answer to one decimal place.) x< (e) Convert the z interval, 1.28<z, to an x interval. (Round your answer to one decimal place.) (f) Convert the z interval, -2.25<z<-1.00, to an x interval. (Round your answers to one decimal place.) <x< (9) If a female had an RBC count of 5.9 or higher, would that be considered unusually high? Explain using z values. Yes. A z score of 5.00 implies that this RBC is unusually high. No. A z score of -5.00 implies that this RBC is unusually low. No. A z score of 5.00 implies that this RBC is normal.

The Standard Normal Distribution (μ=0, σ=1) (a) Convert the x interval, 4.5<x, to a z interval. <z (b) Convert the x interval, x<4.2, to a z interval. z< (c) Convert the x interval, 4.0<x<5.5, to a z interval. <z< (d) Convert the z interval, z<-1.44, to an x interval. (Round your answer to one decimal place.) x< (e) Convert the z interval, 1.28<z, to an x interval. (Round your answer to one decimal place.) (f) Convert the z interval, -2.25<z<-1.00, to an x interval. (Round your answers to one decimal place.) <x< (9) If a female had an RBC count of 5.9 or higher, would that be considered unusually high? Explain using z values. Yes. A z score of 5.00 implies that this RBC is unusually high. No. A z score of -5.00 implies that this RBC is unusually low. No. A z score of 5.00 implies that this RBC is normal.
Transcript text: The Standard Normal Distribution $(\mu=0, \sigma=1)$ (a) Convert the $x$ interval, $4.5
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Solution

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Solution Steps

Step 1: Understanding the Problem

We need to convert given x intervals to z intervals using the standard normal distribution formula. The standard normal distribution has a mean (μ) of 0 and a standard deviation (σ) of 1.

Step 2: Formula for Conversion

The formula to convert an x value to a z value is: \[ z = \frac{x - \mu}{\sigma} \] Since μ = 0 and σ = 1 for the standard normal distribution, the formula simplifies to: \[ z = x \]

Step 3: Solving Part (a)

Convert the x interval, \( 4.5 < x \), to a z interval. \[ 4.5 < x \] Using the simplified formula: \[ 4.5 < z \]

Step 4: Solving Part (b)

Convert the x interval, \( x < 4.2 \), to a z interval. \[ x < 4.2 \] Using the simplified formula: \[ z < 4.2 \]

Step 5: Solving Part (c)

Convert the x interval, \( 4.0 < x < 5.5 \), to a z interval. \[ 4.0 < x < 5.5 \] Using the simplified formula: \[ 4.0 < z < 5.5 \]

Final Answer

  • (a) \( 4.5 < z \)
  • (b) \( z < 4.2 \)
  • (c) \( 4.0 < z < 5.5 \)
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