MATH LAB – QNT – DUE IN 3 HOURS (11:30PM EST)

FIND THE FOLLOWING PROBABILITIES FOR THE STANDARD NORMAL RANDOM VARIABLE Z. (ROUND TO 3 DECIMAL PLACES AS NEEDED)

a.  P (Z > 1.44) =    

b.  P (Z < -1.59) =

c.  P (0.48 < = Z <= 2.66) =

d.  P ( -2.31 < Z < 1.21) = 

 

2.  FIND THE AREA UNDER THE STANDARD NORMAL PROBABILITY DISTRIBUTION BETWEEN THE FOLLOWING PAIRS OF Z-SCORES. (ROUND TO 3 DECIMAL PLACES AS NEEDED)

a.  z = 0 and z = 2.00, the area under the standard normal probability distribution is _________

b.  z = 0 and z = 3.00,  the area under the standard normal probability distribution is _________

c.  z = 0 and z = 1.00,  the area under the standard normal probability distribution is _________

d.  z = 0 and z = 0.62,  the area under the standard normal probability distribution is _________

 

3.  FIND THE AREA UNDER THE STANDARD NORMAL PROBABILITY DISTRIBUTION BETWEEN THE FOLLOWING PAIRS OF Z-SCORES. (ROUND TO 3 DECIMAL PLACES AS NEEDED)

a.  z = 0 and z = 3.00, the area under the standard normal probability distribution is _________

b.  z = 0 and z = 1.00,  the area under the standard normal probability distribution is _________

c.  z = 0 and z = 2.00,  the area under the standard normal probability distribution is _________

d.  z = 0 and z = 0.74,  the area under the standard normal probability distribution is _________

 

4. FIND THE FOLLOWING PROBABILITY FOR THE STANDARD NORMAL RANDOM VARIABLE Z.  (ROUND TO 3 DECIMAL PLACES AS NEEDED)

 

P(-3<= Z<=3)

 

5. SUPPOSE THE RANDOM VARIABLE X IS BEST DESCRIBED BY A NORMAL DISTRIBUTION WITH u=29 AND o=5. FIND THE Z SCORES THAT CORRESPONDS TO EACH OF THE FOLLOWING X-VALUES.  (ROUND TO 2 DECIMAL PLACES AS NEEDED)

a.  x = 19  is z =

b.  x = 29  is z =

c.  x = 14  is z =

d.  x = 15  is z =

e. x = 23   is z =

f.  x = 35   is z = 

 

6.  SUPPOSE X IS A NORMALLY DISTRIBUTED RANDOM VARIABLE WITH u = 12 AND o = 2. FIND EACH OF THE FOLLOWING PROBABILITIES.

a.  P(x>= 13.5) =

b. P(x<= 8.5) =

c. P(12.56<=x<=16.82) =

d. P(6.82<=x<=15.48) =

 

7.  THE AGES OF A GROUP OF 50 WOMEN ARE APPROXIMATELY NORMALLY DISTRIBUTED WITH A MEAN OF 48 YEARS AND A STANDARD DEVIATION OF 6 YEARS. ONE WOMAN IS RANDOMLY SELECTED FROM THE GROUP AND HER AGE IS OBSERVED.

a. Find the probability that her age will fall between 55 and 60 years. The probability is  ________________

b. Find the probability that her age will fall between 47 and 53 years. The probability is  ________________

c.  Find the probability that her age will be less than 34 years. The probability is  ________________

d.  Find the probability that her age will exceed 40 years. The probability is  ________________

 

8.  FINANCIAL ANALYST WHO MAKE FORECASTS OF STOCK PRICES ARE CATEGORIZD AS EITHER “BUY-SIDE” ANALYST OR “SELL-SIDE” ANALYST. THE MEAN AND STANDARD DEVIATION OF THE FORECAST ERRORS FOR BOTH TYPES OF ANALYSTS ARE SHOWN IN THE TABLE TO THE RIGHT. ASSUME THAT THE DISTRIBUTION OF FORECAST ERRORS ARE APPROXIMATELY NORMALLY DISTRIBUTED.

 

                             BUY-SIDE ANALYST    SELL-SIDE ANALYST

MEAN                            0.83                                    -0.07

STANDARD                 1.92                                     0.84

DEVIATION

 

a,  Find the propability that a buy-side analyst has a forecast error of  +2.01 or higher. The probability is ______

b.  Find the propability that a sell-side analyst has a forecast error of  +2.01 or higher. The probability is ______

 

9. THE MEAN GAS MILEAGE FOR A HYBRID CAR IS 57 MILES PER GALLON. SUPPOSE THAT THE GASOLINE MILEAGE IS APPROXIMATELY NORMALLY DISTRIBUTED WITH A STANDARD DEVIATION OF 3.5 MILES PER GALLON.

a. What is the probability that the randomlyselectedhybrid gets more than 61 miles per gallon? The probability is 

b.  What is the probability that a randomly selected hybrid gets 53 miles per gallon or less? The probability is

c. What is the probability that randomly selected hybrid gets between 58 and 62 miles per gallon? The probability is

d. What is the probability that a randomly selected hybrid gets less than 45 miles per gallon? The probability is

 

10.  RESOURCE RESERVATION PROTOCOL (rsvp) WAS ORIGINALLY DESIGNED TO ESTABLISH SIGNALING LINKS FOR STATIONARY NETWORKS. RSVP WAS APPLIED TO MOBILE WIRELESS TECHNOLOGY. A SIMULATION STUDY REVEALED THAT THE TRANSMISSION DELAY (MEASURED IN MILLISECONDS) OF AN RSVP LINKED WIRELESS DEVICES HAS AN APPROXIMATE NORMAL DISTRIBUTION WITH MENU u=49.5 MILLISECONDS AND o= 8.5 MILLISECONDS. 

 

a. What is the probability that the transmission delay is less than 57 milliseconds?