Question

Let ( x ) be ( x² ). Approximate ( P(150 < x < 250) ).

A. P(15000 < x < 25000)
B. P(125 < x < 225)
C. P(22500 < x < 62500)
D. P(12 < x < 22)

Answer 1

The approximate probability P(150 < x < 250) when (x) is (x²) is found by squaring the bounds, giving us P(22500 < x < 62500), which corresponds to answer choice C.

Step-by-step explanation:

To approximate P(150 < x < 250) given the transformation (x) is (x²), we first need to square the values 150 and 250 to reframe the question in terms of the squared variable. Squaring 150 gives us 150² = 22500, and squaring 250 gives us 250² = 62500. Therefore, the transformed probability is P(22500 < x < 62500), which corresponds to answer choice C.

You can verify this by using a graphing calculator, software, or a binomial table to find the equivalent probabilities. However, for this question, the transformation is straightforward and does not require any calculation other than squaring the two bounds of the inequality.