Answer:
a)
<em>The probability that a newborn elephant weighs between 250 and 275 pounds</em>
<em>P(250≤ x ≤275) = 0.1577</em>
b)
<em>The probability that a newborn elephant weighs more than 210 pounds</em>
<em>P(x >210 ) = 0.6293</em>
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given mean of the Population = 225
Given standard deviation of the population = 45
Let 'X' be the random variable in normal distribution
Let x₁ = 250
Let x₂ = 275
<em>The probability that a newborn elephant weighs between 250 and 275 pounds</em>
P(250≤ x ≤275) =P(0.55≤ Z≤1.11)
= P(Z≤1.11) - P(Z≤0.55)
= 0.5 + A( 1.11) - ( 0.5 + A(0.55)
= A(1.11) - A(0.55)
= 0.3665 - 0.2088
= 0.1577
<u><em>Step(ii):-</em></u>
<em>The probability that a newborn elephant weighs between 250 and 275 pounds</em>
<em>P(250≤ x ≤275) = 0.1577</em>
b)
Let x = 210
The probability that a newborn elephant weighs more than 210 pounds
P(x >210 ) = P( Z> -0.33)
= 1- P( Z < -0.33)
= 1 - ( 0.5 - A(-0.33))
= 0.5 + A( -0.33)
= 0.5 + A(0.33) (∵ A(-0.33) = A(0.33)
= 0.5 + 0.1293
= 0.6293
<u><em>Final answer:-</em></u>
<em>The probability that a newborn elephant weighs more than 210 pounds</em>
<em>P(x >210 ) = 0.6293</em>