the probability of 17-year-old girl in the US that are between 58.4 inches and 69.6 inches is 0.9544 .
Explanation:
Step 1: Sketch the curve.
The probability that 58.4<X<69.6 is equal to the blue area under the curve.
Step 2:
Since μ=64 and σ=2.8 we have:
P ( 58.4<X<69.6 ) = P ( 58.4−64 < X−μ < 69.6−64 )=P ( 58.4−64/2.8 < X−μ/σ< 69.6−64/2.8)
Since Z = x−μ/σ , 58.4−64/2.8=−2 and 69.6−64/2.8=2 we have:
P ( 58.4<X<69.6 )=P ( −2<Z<2 )
Step 3: Use the standard normal table to conclude that:
P ( −2<Z<2 )=0.9544
Therefore, the probability of 17-year-old girl in the US that are between 58.4 inches and 69.6 inches is 0.9544 .