Questions: Question 5 0 / 2 pts 3 ↔ 99 Details The arrows can only be dragged to z scores that are accurate to 1 place after the decimal point (these values correspond to the tick marks on the horizontal axis). Select from the drop down menu to shade to the left, to the right, between or left and right of the z-score. You may round probabilities to three decimal places. a) Sketch the region corresponding to the statement P(-0.9<Z<1.5) Shade: Left of a value v̂. Click and drag the arrows to adjust the values. b) Find P(-0.9<Z<1.5)

Solution Steps

The problem requires us to find the probability for the range \(-0.9 < Z < 1.5\). The Z-scores are \(-0.9\) and \(1.5\).

Look up the cumulative probabilities for the Z-scores in the standard normal distribution table:

• For \(Z = -0.9\), the cumulative probability is approximately \(0.1841\).
• For \(Z = 1.5\), the cumulative probability is approximately \(0.9332\).

To find the probability that \(Z\) is between \(-0.9\) and \(1.5\), subtract the cumulative probability at \(-0.9\) from the cumulative probability at \(1.5\): \[ P(-0.9 < Z < 1.5) = P(Z < 1.5) - P(Z < -0.9) \] \[ P(-0.9 < Z < 1.5) = 0.9332 - 0.1841 \] \[ P(-0.9 < Z < 1.5) = 0.7491 \]

Final Answer