Question

Solve the problem. Assume that Z e normally distributed with parameters, (u = 0, 0 = 1). If P(-k<Z<k) - 0.06376, find k. 0.18 0.08 1.64 1.49 Moving to another question will save this response.

Answer 1

The correct option is the second option: 0.08 [ANSWER]

Explanation:

We are given that:

P(-k<Z <k) → P(Z <k) - P(Z <-k) → P(Z <k) - P(Z > k) = 0.06376 = 0.06376 = 0.06376 [Since, the normal distribution is symmetric about the mean, we have: P(Z - <-k) = P(Z -> k) = P(Z -0<-k) = P(Z -0 > k) → P(Z <-k) = P(Z > k)] = P(Z <k) – [1 – P(Z <k)] = 0.06376 → P(Z <k) - 1+ P(Z <k) = 0.06376 = 2P(Z <k) = 0.06376 +1 1.06376 → P(Z <k) 2 = P(Z <k) = 0.53188 From the table of standard normal distribution, we get: P(Z < 0.08) = 0.53188 Thus, from the last two equations, we get: k = 0.08 ANSWER

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