Problem workshop 1

Mean weight of 500 male students at sfu is 151 lbs (non engineers)

• SD= 15 lbs • Assume weight follows normal distribution • (a) what probability of weight between 119.5 and 155.5 lbs • (b) Number of student >=185.5 lbs

We can assume that its a Normal Distribution (gaussian)

• so we can assume that the
  • $\mu =151$ (mean), $\sigma =15$ (sd)

• A)

  • we can assume that the upper bound we want for z is 155.5, and the lower to be 119.5
    • $z_{min}=\frac{x-\mu }{\sigma }=\frac{119.5-151}{15}=-2.10$, x=119.5
      • this is in terms of std so it would be 2 to the left
    • $z_{max}=\frac{x-\mu }{\sigma }=\frac{155.5-151}{15}=0.30$ x=155.5
      • this is in terms of std
  • now using that we calculate the probability of both
    • $P(Z_{max})=\frac{1}{2}\left[1+erf\left(\frac{0.3}{\sqrt{2}}\right)\right]=0.6179$
    • $P(Z_{min})=\frac{1}{2}\left[1+erf\left(-\frac{2.10}{\sqrt{2}}\right)\right]=0.0179$
      • $P=P(Z_{max})-P(Z_{min})=0.600$ so it would be 60% in that weight range

• B)

  • we know in the CDF we choose everything under that, so we can just 1-CDF so its the inverse