0.9544 is the probability that a randomly selected student’s math score is between 300 and 700 .
<u>Step-by-step explanation:</u>
Step 1: Sketch the curve.
The probability that 300<X<700 is equal to the blue area under the curve.
Step 2:
Since μ=500 and σ=100 we have:
P ( 300<X<700 )=P ( 300−500< X−μ<700−500 )
⇒P ( 300−500/100 < X−μ/σ < 700−500/ 100)
Since Z = x − μ /σ , 300−500 /100 = −2 and 700−500/100 = 2 we have:
P ( 300<X<700 )=P ( −2<Z<2 )
Step 3: Use the standard normal table to conclude that:
P ( −2<Z<2 )=0.9544
Therefore,0.9544 is the probability that a randomly selected student’s math score is between 300 and 700 .
