1. Consider the discrete probability distribution to the right when answering th

Question

1. Consider the discrete probability distribution to the right when answering the following question. find the probability the x equals 4.

X =2 ,P(x) = 0.04

x =4 P(x) = ?

x = 6 P(x) = 0.31

x = 8 P(x) = 0.01

a 0.36

b. 2.36

c. 0.64

d. 1.44

2. A new phone system was installed last year to help reduce the expense of personal calls that were being made by employees.before the system was installed the amount being spent on personal calls followed a normal distribution with a mean of $700 per month and a standard deviation of $50 per month. refer to such expenses as PCEs (Personal call expenses). Using the distribution above what is the probability that a randomly selected month had a PCE of between $575 and $790?

a. 0.421

b. .9579

c. .0001

d. .9999

3. The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1600 miles. what is the probability a particular tire of this brand will last longer than 58400 miles?

a. .1587

b. .2266

c. .7266

d. 8413

4. The amount of corn chips dispensed into a 32-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 32.5 ounces and a standard deviation of 0.2 ounce. What chip amount represents the 67th percentile for the bag weight distribution?

a. 32.63 oz

b. 32.13 oz

c. 32.59 oz

d. 32.09 oz

5. The amount of soda a dispensing machine pours into a 12 ounce can of soda follows a normal distribution with a mean of 12.24 ounces and a standard deviation of 0.16 ounce, the cans only hold 12.40 ounces of soda. Every can that has more than 12. 40 ounces of soda poured into ir causes a spill and the can needs to go through a special cleaning process before it can be sold. what is the probability a randomly selected can will go through this process?

a. .1587

b. .3413

c. .6587

d .8413

Explanation / Answer

Ans:

1)Option c is correct.

P(x=4)=1-(0.04+0.31+0.01)=1-0.36=0.64

3)

z score=(58400-60000)/1600=-1600/1600=-1

P(z>-1)=1-P(z<-1)=1-0.1587=0.8413

Option d is correct.

4)67th percentile means that

P(Z<=z)=0.67

z=0.4399

x=32.5+0.4399*0.2=32.5879

x=32.59

Option c is correct.

5)P(x>12.4)

z score=(12.4-12.24)/0.16=0.16/0.16=1

P(z>1)=1-P(z<1)=1-0.8413=0.1587

Option a is correct.

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