ull Ultra 4:02 PM @ 92%.-. + Elementary Statistics Midterm B Fall 2017 Name Show

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ull Ultra 4:02 PM @ 92%.-. + Elementary Statistics Midterm B Fall 2017 Name Show your work in the blue books. Keep your eyes on your own paper Any talking to another student will cancel your test 3. The following chart compares occupations with salaries Occupation 40,000 or less 41 to 70,000 71 to 100,000More than 100.000 Total 95 100 25 20 20 35 30 20 30 10 95 345 Find the probability that a person selected from this group at random is a) a nurse b) a lawyer earning more than 100,000 c) a Doctor or someone earning between 41,000 and 70.000 d) a nurse and a Doctor e) A lawyer or someone earning between71,000 and 100,000 ) an accountant given that they earn between 41,000 and 70,000 e) a person earning 40,000 or less given that they are aDoctor S points 5points S points 4. The time it takes for bables to learn to walk is known to be normally distributed with mean 8 months and standard deviation of 1.5 months. What percent of babies learn to walk a) between 9 and 12 months, inclusive) B more than 10 months. c) less than 7 months d) If the longest 2.5% are considered to be "late bloomers. how many 5 points 5 points 5 points 5points months constitutes a late bloomer eir the shortest 2.5% are considered as "ahead of their time, how 5 points many months constitutes being "ahead of their time Answer all please ASAP

Explanation / Answer

3)

probability that a person selected from the group at random is

a) Nurse

probability = 55/345 =0.15942

b) A lawyer earning more than the 1,00,000

probability = 50/345 = 0.14492

c) A doctor or someone who earning between 41000 to 70000 then doctor or nurse earning between 41000 and 70000

probability =20/345+20/345 = 40/345 = 0.11594

d)A nurse and a doctor

probability = (55/345)*(100/345)= 0.04620

e)A lawyer or someone(doctor) earning between 71000 and 100000

probability = 30/345 + 30/345 = 0.17391

f)An accountant earning between 41000 and 70000

probability = 25/345= 0.0724

g)

A person earning 40000 or less that they are doctor

probability = 10/345 =0.0289

4.

NORMAL DISTRIBUTION

the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2

standard normal distribution is a normal distribution with a,

mean of 0,

standard deviation of 1

equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)

mean ( u ) = 8

standard Deviation ( sd )= 1.5

a)

To find P(a < = Z < = b) = F(b) - F(a)

P(X < 9) = (9-8)/1.5

= 1/1.5 = 0.6667

= P ( Z <0.6667) From Standard Normal Table

= 0.7475

P(X < 12) = (12-8)/1.5

= 4/1.5 = 2.6667

= P ( Z <2.6667) From Standard Normal Table

= 0.9962

P(9 < X < 12) = 0.9962-0.7475 = 0.2487

b)

P(X > 10) = (10-8)/1.5

= 2/1.5 = 1.3333

= P ( Z >1.3333) From Standard Normal Table

= 0.0912

c)

P(X < 7) = (7-8)/1.5

= -1/1.5= -0.6667

= P ( Z <-0.6667) From Standard Normal Table

= 0.2525

d)

P ( Z > x ) = 0.025

Value of z to the cumulative probability of 0.025 from normal table is 1.96

P( x-u / (s.d) > x - 8/1.5) = 0.025

That is, ( x - 8/1.5) = 1.96

--> x = 1.96 * 1.5+8 = 10.9399 months constitutes late bloomers

e)

P ( Z < x ) = 0.025

Value of z to the cumulative probability of 0.025 from normal table is -1.96

P( x-u/s.d < x - 8/1.5 ) = 0.025

That is, ( x - 8/1.5 ) = -1.96

--> x = -1.96 * 1.5 + 8 = 5.0601 months constitutes being ahead of their time

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