2. Let Z be a random variable with a standard normal distribution. Calculate: P(Z ≥ 1.98)= ? P(Z <− 2.77)= ? P(−3.19 ≤ Z ≤− 3.03)= ? P(Z ≤ −0.15 or Z ≥ 0.99)= ? If P(Z < k)=0.14, then the value of k is:? If P(Z > k)=0.89, then the value of k is:? Note: Answer with at least 4 decimal places
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2. Let Z be a random variable with a standard
Calculate:
- P(Z ≥ 1.98)= ?
- P(Z <− 2.77)= ?
- P(−3.19 ≤ Z ≤− 3.03)= ?
- P(Z ≤ −0.15 or Z ≥ 0.99)= ?
- If P(Z < k)=0.14, then the value of k is:?
- If P(Z > k)=0.89, then the value of k is:?
Note: Answer with at least 4 decimal places
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- If X is a normal random variable with mean μ = 3 and standard deviation σ = a. P(X > 11) b. P(2-3|X > -5) 4, findSuppose X is a normal random variable with mean u = 17.5 and o = 6. A random sample of size n = 24 is selected from this population. a. Find the distribution of b. Find P(X < 14) and P(X < 14) Find P(15If z is a standard normal random variable and P(-zyLet the r.v. Z have the standard normal distribution. Find (i) P(Z≤-2.15) (ii) P (Z≥ 1.96) (iii) P (-1.96≤ ? ≤ −0.84) (iv) P (-1.30≤ ? ≤ 2.18) (v) P (0≤ ? ≤ 1.20)Let X be a normally distributed random variable with mean u = 27 and standard deviation o = 2. Calculate P(X < 21). Calculate P(25Can the normal distribution be used to approximate the random variable x? O A. No, because nq < 5. O B. No, because np < 5. O C. Yes, because np 25 and nq 2 5. O D. No, because np < 5 and nq < 5.3. If Z is a random variable having the standard normal distribution, find i. P(Z - 1.08) iii. P(-1.90Q2The random variable X has a uniform distribution with values between 14 and 22. What is the mean and standard deviation of X? (Round your answer to three decimal places.) Select the correct answer below: mean is 18; standard deviation is 83≈2.667 mean is 14; standard deviation is 46–√3≈3.266 mean is 18; standard deviation is 43–√3≈2.309 mean is 14; standard deviation is 83≈2.667 mean is 14; standard deviation is 43–√3≈2.309 mean is 18; standard deviation is 46–√3≈3.266If a random variable X follows normal distribution with mean 10 and standard deviation 50, write down its p.d.f. Also calculate P(X 10). -x? 2 e |Given: 4(1.96) = 0.975, þ(2.36) = 0.99, where (Z) = -dz] ov2nThe random variable x has a normal distribution with mean 50 and variance 9. Find the value of x, call it x0, such that: a) P(x ≤ xo) = 0.8413 b) P(x > xo) = 0.025 c) P(x > xo) = 0.95 d) P(41 ≤ x ≤ xo) = 0.8630The random variable X has a pdf f(x) = 5x 0≤x≤ 0.6325. What is the median of X 0.316 0.333 0.350 0.500 0.447 No answerSEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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