ndp","difficulty":"medium","question_text":"If $X \\sim N(0, 1)$, what is $P(|X| < 1)$?","choices":[{"id":"a","text":"$$2\\Phi(1) - 1$"},{"id":"b","text":"$$\\Phi(1)$"},{"id":"c","text":"$$1 - \\Phi(1)$"},{"id":"d","text":"$$0.5\\Phi(1)$"}],"correct_ids":["a"],"solution":"**Step 1:** $P(|X| < 1) = P(-1 < X < 1) = \\Phi(1) - \\Phi(-1)$.\n\n**Step 2:** By symmetry, $\\Phi(-1) = 1 - \\Phi(1)$.\n\n**Step 3:** $\\Phi(1) - (1 - \\Phi(1)) = 2\\Phi(1) - 1$.","created_at":"2026-06-11T16:46:52.041696+00:00","updated_at":"2026-06-11T16:46:52.041696+00:00","diagram_svg":null,"human_approved":false,"user_approved":false,"ai_approved":false,"ai_review":null,"topic":{"name":"Distributions","slug":"probability_distributions","description":"Binomial, normal, uniform, Poisson"}},"user":null,"initialGuestCount":0}]}]]}] f:[["$","meta","0",{"name":"viewport","content":"width=device-width, initial-scale=1"}],["$","meta","1",{"charSet":"utf-8"}],["$","title","2",{"children":"Ononot — If X \\sim N(0, 1), what is P(|X| < 1)?"}],["$","meta","3",{"name":"description","content":"If X \\sim N(0, 1), what is P(|X| < 1)?"}],["$","meta","4",{"name":"robots","content":"index, follow"}],["$","link","5",{"rel":"canonical","href":"https://ononot.com/questions/if-x-sim-n0-1-what-is-px-1-77ndp"}],["$","meta","6",{"property":"og:title","content":"Ononot — If X \\sim N(0, 1), what is P(|X| < 1)?"}],["$","meta","7",{"property":"og:description","content":"If X \\sim N(0, 1), what is P(|X| < 1)?"}],["$","meta","8",{"property":"og:url","content":"https://ononot.com/questions/if-x-sim-n0-1-what-is-px-1-77ndp"}],["$","meta","9",{"property":"og:type","content":"website"}],["$","meta","10",{"name":"twitter:card","content":"summary"}],["$","meta","11",{"name":"twitter:title","content":"Ononot — If X \\sim N(0, 1), what is P(|X| < 1)?"}],["$","meta","12",{"name":"twitter:description","content":"If X \\sim N(0, 1), what is P(|X| < 1)?"}],["$","link","13",{"rel":"icon","href":"/favicon.ico","type":"image/x-icon","sizes":"16x16"}]] 4:null

If X∼N(0,1)X \sim N(0, 1)X∼N(0,1), what is P(∣X∣<1)P(|X| < 1)P(∣X∣<1)?

If $X \sim N(0, 1)$ , what is $P(|X| < 1)$ ?