Question

Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.) P(−2.10 ≤ z ≤ −0.46)

Answer 1

solution:

1) Given that

'Z' be a random variable with a Standard Normal Distribution

we know that In  Standard Normal Distribution   

Mean =0 and Standard Deviation = 1

P(−2.10 ≤ z ≤ −0.46) = P(-0.46) - P(-2.10)

= [1-P(0.46)] - [1-P(2.10)]

= 1 - P(0.46) - 1 + P(2.10)

= P(2.10) - P(0.46)

= 0.4821 - 0.1772 [since,using standard normal distribution table ]

= 0.3049

    P(−2.10 ≤ z ≤ −0.46) = 0.3049

The graph of P(−2.10 ≤ z ≤ −0.46)   would be as P(0.46 ≤ z ≤ 2.10)