Find
a. P(Z=1.32)
b. P(Z>5)
c. P(-1<Z<1)
d. P(-2<Z<2)
e. P(-3<Z<3)
(c, d, and e form what is called the Empirical Rule. Look it up!)
f. The 20th percentile of Z
g. The z value with 5% area to its right.
please show all work not just answers and do all of them please and thank you will rate high
a) P(Z = 1.32) = 0
b) P(Z > 5) = 1 - P(Z < 5)
= 1 - 1 = 0
c) P(-1 < Z < 1)
= P(Z < 1) - P(Z < -1)
= 0.8413 - 0.1587
= 0.6826
According to the Empirical rule about 68% of the data will fall between 1 standard deviation from the mean.
d) P(-2 < Z < 2)
= P(Z < 2) - P(Z < -2)
= 0.9772 - 0.0228
= 0.9544
According to the Empirical rule about 95% of the data will fall within 2 standard deviation from the mean.
e) P(-3 < Z < 3)
= P(Z < 3) - P(Z < -3)
= 0.9987 - 0.0013
= 0.9974
According to the Empirical rule all of the data (about 99.7%) will fall within 3 standard deviation from the mean.
f) P(Z < z) = 0.2
or, z = -0.84
g) P(Z > z) = 0.05
or, 1 - P(Z < z) = 0.05
or, P(Z < z) = 0.95
or, z = 1.645
Find a. P(Z=1.32) b. P(Z>5) c. P(-1<Z<1) d. P(-2<Z<2) e. P(-3<Z<3) (c, d, and e form...
Section P.5: Density Curves and the Normal Distribution Example 1: Find the specified areas for a standard normal density, and sketch the area. (a) The area below z = 0.8 (b) The area above z = 1.2 (c) The area between z = -1 and z = 2 Example 2: Find endpoints on a standard normal density with the given property, and sketch the area. (a) The area to the left of the endpoint is about 0.20. (b) The area...
2. Random variable Z has the standard normal distribution. Find the following probabilities a): P[Z > 2] b) : P[0.67 <z c): P[Z > -1.32] d): P(Z > 1.96] e): P[-1 <Z <2] : P[-2.4 < Z < -1.2] g): P[Z-0.5) 3. Random variable 2 has the standard normal distribution. Find the values from the following probabilities. a): P[Z > 2) - 0.431 b): P[:<] -0.121 c): P[Z > 2] = 0.978 d): P[2] > 2] -0.001 e): P[- <Z...
1) If 3iis a zero of p(z)=az2+z3+bz−27, find the real numbers a and b. Enter them in the form a,b 2) Factorise p(z)=z3−2z2+z−2 into linear factors. Enter them in the format z+3+I, z-6+5*I. 3) Consider p(z)=iz2+z3−2iz−4z2+i+5z−2. Given that z=2−i is a zero of this polynomial, find all of its zeros. Enter them in the form 2+3*I, 4+5*I, 6-7*I
5. Suppose demand is of the form D(p)-a - b p (a) Find the function for marginal revenue for a monopolist. Hint: this is known as the twice as steep rule, and it always applies to linear demand functions for a monopolist. (b) Suppose the firm faces a constant marginal cost, denoted mc. What is the equilibrium price, quantity producer surplus, consumer surplus, and deadweight loss in terms of parameters a, b, and mc if the firm sets the same...
(4) Given Z N(0, 1) find the following: (a) P(Z 2 1.4) (b) P(Z> 0.75) (c) P(IZI S 2) (d) P(IZ 2 2) (e) Find z such that P(Z < z) = 0.11 (f) Find z such that P(Z > z) = 0.02
Diagonalize a. b. c. d. e. f. Diagonalize A A = 1 3 4 2 a. A = PDP-1 b. A = PDP-1 1 Р 1 1 OC. A = PDP-1 -1 3 P = 2 5 d. A = PDP-1 -3 1 P= -4 1 e. A = PDP-1 1 -1 P 3 1 Of A = PDP-1 P-[31] -- [6-2] [37] - [64] P=[ +3 z] --[: = D = 10 03
) Find the p(z < −3.45) (a) 1 (b) 0.0003 (c) 0.9997 (d) 0.9974 (e) 0.0
3. Let a, b, c E Z such that ca and (a,b) = 1. Show that (c, b) = 1. 4. Suppose a, b, c, d, e E Z such that e (a - b) and e| (c,d). Show that e (ad — bc). 5. Fix a, b E Z. Consider the statements P: (a, b) = 1, and Q: there exists x, y E Z so that ax + by = 1. Bézout’s lemma states that: if P, then...
Consider p(z) = 2 i 22 + x3 – 4 iz-4-2 +2 i +5 z– 2. Given that z= 2 – 2 i is a zero of this polynomial, find all of its zeros. Enter them in the form 2+3*1, 4+5*1, 6-7*|
3. Let Z be a continuous random variable with Z-N(0,1). (a) Find the value of P(Z <-0.47). (b) Find the value of P(Z < 2.00). Note denotes the absolute value function. (c) Find b such that P(Z > b) = 0.9382. (d) Find the 27th percentile. (e) Find the value of the critical value 20.05-