The average height of a 17-year-old girl in the US is about 64 inches with a
standard deviation of 2.8 inches. Without using a calculator, estimate the
probability of 17-year-old girl in the US that are between 58.4 inches and 69.6
inches.

the probability of 17-year-old girl in the US that are between 58.4 inches and 69.6 inches is 0.9544 .

Step-by-step 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 .