Question

Which of the following is correct ? * If 0 > − 7 , then 0 1 , then − 8 > − 1 If − 4 5

Answer 1

Step-by-step explanation:

$Let X = length, in seconds, of an eight-week-old baby’s smile. \\ </p><p></p><p>The notation for the uniform distribution is X ~ U(a, b) where a = the lowest value of x and b = the highest value of x. \\ </p><p></p><p>The probability density function is \\ </p><p>f</p><p>(</p><p>x</p><p>)</p><p>=</p><p>1</p><p>b</p><p>−</p><p>a</p><p>f(x)=1b−a for a ≤ x ≤ b. \\ </p><p></p><p>For this example, \\ X ~ U(0, 23) and</p><p>f</p><p>(</p><p>x</p><p>)</p><p>=</p><p>1</p><p>23</p><p>−</p><p>0</p><p>f(x)=123−0 for 0 ≤ X ≤ 23. \\ </p><p></p><p>Formulas for the theoretical mean and standard deviation are \\ </p><p>μ</p><p>=</p><p>a</p><p>+</p><p>b</p><p>2 \\ </p><p>and \\ </p><p>σ</p><p>=</p><p>√</p><p>(</p><p>b</p><p>−</p><p>a</p><p>)</p><p>2</p><p>12 \\ </p><p>μ=a+b2andσ=(b−a)212 \\ </p><p>For this problem, the theoretical mean and standard deviation are \\ </p><p>μ</p><p>=</p><p>0</p><p>+</p><p>23</p><p>2</p><p>=</p><p>11.50</p><p> seconds \\ </p><p>and \\ </p><p>σ</p><p>=</p><p>√</p><p>(</p><p>23</p><p>−</p><p>0</p><p>)</p><p>2</p><p>12</p><p>=</p><p>6.64</p><p> seconds \\ </p><p>μ=0+232=11.50 \\ secondsandσ=(23−0)212=6.64 seconds \\ </p><p>Notice that the theoretical mean and standard deviation are close to the sample mean and standard deviation in this example.$