The area to the right of z is 0.3300. For the standard normal random variable z,

Question

The area to the right of z is 0.3300. For the standard normal random variable z, find z for each situation. a. The area to the left of z is 0.2119. b. The area between -z and z is 0.9030 c. The area between -z and z is 0.2052. d. The area to the left of z is 0.9948 e. The area to the right of z is 0.6915. f. 23. The demand for a new product is estimated to be normally distributed with = 200 and 40. Let x be the number of units demanded, and find the following probabilities: a. P(180 sx s 220) b. P(r 250) c. P(r s 100) d. P(225 s s 250) 24. 5. The College Board National Office recently reported that in 2011-2012, the 547.038 high school juniors who took the ACT achieved a mean score of 530 with a standard deviation of 123 on the mathematics portion of the test (http://media.collegeboard.com/digitalServices/pdf /research/2013/TotalGroup-2013.pdf). Assume these test scores are normally distributed a. What is the probability that a high school junior who takes the test will score at least 610 0 b. What is the probability that a high school junior who takes the test will score no higher c. What is the probability that a high school junior who takes the test will score between d. How high does a student have to score to be in the top 1()% of high school juniors on on the mathematics portion of the test? than 460 on the mathematics portion of the test? 460 and 550 on the mathematics portion of the test? the mathematics portion of the test?

Explanation / Answer

Result:

23).

a). z= -0.8

b). z = 1.66

c). z = 0.26

d). z = 2.562

e). z= -0.5

24).

a).

Z value for 180, z =(180-200)/40 = -0.5

Z value for 220, z =(220-200)/40 = 0.5

P( 180x220) = P( -0.5<z<0.5) = P( z < 0.5) – P( z< -0.5)

= 0.6915-0.3085

=0.383

b).

Z value for 250, z =(250-200)/40 = 1.25

P( x 250) =P( z > 1.25)

=0.1056

c).

Z value for 100, z =(100-200)/40 = -2.5

P( x 100) =P( z <2.5)

=0.9938

d).

Z value for 225, z =(225-200)/40 = 0.625

Z value for 250, z =(250-200)/40 = 1.25

P( 225x250) = P( 0.625<z<1.25) = P( z < 1.25) – P( z< 0.625)

= 0.8944- 0.734

=0.1604

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.