Question

SAT scores probability 1​

Answer 1

Answer:

  a.  81.5%

Step-by-step explanation:

The z-score for 400 is ...

  Z = (X -μ)/σ = (400 -500)/100 = -1

The z-score for 700 is ...

  Z = (700 -500)/100 = 2

The empirical rule tells you that 68% of the distribution is within ±1σ of the mean, and 95% is within ±2σ of the mean. Half of that first number is in the range Z = -1 to 0, and half that second number is in the range Z = 0 to +2. So, the probability you want is ...

  (1/2)(68%) + (1/2)(95%) = 81.5% . . . . matches choice A