Answer to Question #255690 in Statistics and Probability for Pro

Question #255690
The mean weight of 800 college students is 56 kg and the standard deviation is 5 kg. Assuming that the weight is normally distributed, determine how many students weigh: a. Between 60 kg and 70 kg. b. More than 68 kg.
1
Expert's answer
2021-10-26T12:47:31-0400

a.

P(60<X<70)=P(X<70)P(X60)P(60<X<70)=P(X<70)-P(X\leq 60)

=P(Z<70565)P(Z60565)=P(Z<\dfrac{70-56}{5})-P(Z\leq \dfrac{60-56}{5})

=P(Z<2.8)P(Z0.8)=P(Z<2.8)-P(Z\leq 0.8)

0.99744490.78814460.209300\approx0.9974449-0.7881446\approx 0.209300

0.209300(800)=1670.209300(800)=167

167 students weigh between 60 kg and 70 kg.


b.


P(X>68)=1P(X68)P(X>68)=1-P(X\leq 68)

=1P(Z68565)=1P(Z2.6)=1-P(Z\leq \dfrac{68-56}{5})=1-P(Z\leq 2.6)

0.004661\approx0.004661

0.004661(800)=40.004661(800)=4

4 students weigh more than 68 kg.



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