Question

In: Statistics and Probability

4. If Z is a standard normal random variable, that is Z ∼ N(0, 1), (a)...

4. If Z is a standard normal random variable, that is Z ∼ N(0, 1), (a) what is P(Z 2 < 1)? (b) Find a number c such that P(Z < c) = 0.75 (c) Find a number d such that P(Z > d) = 0.83 (d) Find a number b such that P(−b < Z < b) = 0.95

Solutions

Expert Solution

a) P(Z < 1.000   ) =   0.8413 (answer)

b)Z value at    0.75   =   0.674   (excel formula =NORMSINV(   0.75   ) )

answer: 0.674

c)P(Z > d) = 0.83

P(Z≤d) = 1-0.83 = 0.17

Z value at    0.17   =   -0.954   (excel formula =NORMSINV(   0.17   ) )

answer: -0.954

d)proportion=   0.9500                      
proportion left    0.0500   is equally distributed both left and right side of normal curve                   
z value at   0.025   = ±   1.960   (excel formula =NORMSINV(   0.05   / 2 ) )  

so, value of b = 1.96

orchestra answered 11 months ago
Next > < Previous

Related Solutions

QUESTION 1 If Z is a standard normal random variable, then P(Z > 0) =   0...
QUESTION 1 If Z is a standard normal random variable, then P(Z > 0) =   0 1 0.4579 0.5 1 points    QUESTION 2 Company A claims that 20% of people in Sydney prefer its product (Brand A). Company B disputes the 20% but has no idea whether a higher or lower proportion is appropriate.  Company B randomly samples 400 people and 88 of them prefer Company A's product (Brand A). Assuming a 5% significance level, which one of the following...
Let z be a standard normal random variable with a mean of 0 and a standard...
Let z be a standard normal random variable with a mean of 0 and a standard devi- ation of 1. Find the following probabilities: (a) P(−0.5<z<0.5) (b) P(−.5<z<1.5) (c) P(−1.5<z<−.75) (d) P(2<z<3)
Find the value of the standard normal random variable z , called z 0 such that:...
Find the value of the standard normal random variable z , called z 0 such that: a)  ?(?≤?0)=0.8998 ?0= (b)  ?(−?0≤?≤?0)=0.676 ?0= (c)  ?(−?0≤?≤?0)=0.198 ?0= (d)  ?(?≥?0)=0.1895 ?0= (e)  ?(−?0≤?≤0)=0.4425 ?0= (f)  ?(−1.11≤?≤?0)=0.8515 ?0=
Find a value of the standard normal random variable z ​, call it z 0​, such...
Find a value of the standard normal random variable z ​, call it z 0​, such that the following probabilities are satisfied. a. ​P(z less than or equals z 0​) equals 0.3027 b. ​P(minus z 0less than or equals z less than z 0​) equals 0.1518 c. ​P(z less than or equals z 0​) equals0.7659 d. ​P(z 0 less than or equals z less than or equals​ 0) equals 0.2706 e. ​P( minus z 0 less than or equals z...
Find the value of the standard normal random variable z, called z subscript 0, such that:...
Find the value of the standard normal random variable z, called z subscript 0, such that: P left parenthesis z greater or equal than z subscript 0 right parenthesis equals.20 Find the value of the standard normal random variable z , called z subscript 0 , such that Find the value of the standard normal random variable z , called z subscript 0 , such that Find the value of the standard normal random variable z , called z subscript...
Find the value of the standard normal random variable z, called z subscript 0, such that:...
Find the value of the standard normal random variable z, called z subscript 0, such that: P left parenthesis z greater or equal than z subscript 0 right parenthesis equals.20 Find the value of the standard normal random variable z , called z subscript 0 , such that Find the value of the standard normal random variable z , called z subscript 0 , such that Find the value of the standard normal random variable z , called z subscript...
Find the value of the standard normal random variable z, called z subscript 0, such that:...
Find the value of the standard normal random variable z, called z subscript 0, such that: P left parenthesis z greater or equal than z subscript 0 right parenthesis equals.20 Find the value of the standard normal random variable z , called z subscript 0 , such that Find the value of the standard normal random variable z , called z subscript 0 , such that Find the value of the standard normal random variable z , called z subscript...
Let z be a random variable with a standard normal distribution. Find P(0 ≤ z ≤...
Let z be a random variable with a standard normal distribution. Find P(0 ≤ z ≤ 0.46), and shade the corresponding area under the standard normal curve. (Use 4 decimal places.)
1. Let  z be a normal random variable with mean 0 and standard deviation 1. What is...
1. Let  z be a normal random variable with mean 0 and standard deviation 1. What is P(-2.25 <  z < -1.1)? 0.1235 0.3643 0.8643 0.4878 You are offered an investment opportunity. Its outcomes and probabilities are presented in the following table. x P(x) -$1,000 .40 $0 .20 +$1,000 .40 ​ 2. The mean of this distribution is _____________. $400 $0 $-400 $200 3. T/F. The probability that the complement of an event will occur is given by P(E') = 1 -...
Let Z ∼ N (0, 1) be a standard normal random variable. Find c by using only one side of the z-table for all questions:
  Let Z ∼ N (0, 1) be a standard normal random variable. Find c by using only one side of the z-table for all questions: (a) P[Z < c] = 0.8980   (b) P[Z > −c] = 0.8980 (c) P[Z > c] = 0.102 (d) P[Z > c] = 0.992 (e) P[Z < −c] = 0.992 (f) P[Z < c] = 0.992   (g) P[|Z| < c] = 0.4246 (h) P[|Z| > c] = 0.1528 (i) P[|Z| < c] = 0.984...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT