Maths multiple problems | Mathematics homework help

4. In a recent statistics class, people’s heights were retrieved, and those
recorded heights (in inches) are the following:

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60 60.24 61.02 61.42 61.82 62 63 64.76 65.75 66.14
66.93 67 68 68 68.11 69 72 72.83 81

Organize the data into a frequency distribution. Let the lower class limit of the first class be 60, and let the class width be 3.

Using the information that you obtained, describe the distribution of the data.

5. A. Find the standard deviation of the data: 1 3 7 9.

B. Find the standard deviation of the data: 4 5 6.

C. Using both answers from A. and B., describe which of the set of data is the denser.

6. Given below are the ages of U. S. presidents when they were inaugurated.

42 43 46 46 47 47 48 49 49 50
51 51 51 51 51 52 52 54 54 54
54 54 55 55 55 55 56 56 56 57
57 57 57 58 60 61 61 61 62 64
64 65 68 69

A. Find P40.

B. Find the percentile of 65.

7. Make a stem plot of the set of data in #6. Then, using the stemplot, please state what the distribution of data may be.

8. A sample of a gasoline station’s records indicates that 385 of 921 gasoline purchases were paid for by credit card. A gasoline purchase is selected at random. What is the probability that it was not paid for by credit card?

9. A standard deck of cards contains 52 cards. Of these, 12 are face cards (kings, queens, and jacks), 26 are black cards (spades and clubs), and 6 are both black and face cards. A card is drawn at random from such a deck. What is the probability that the card is either a black card or a face card?

10. When driving to class, a student must pass 3 traffic lights that operate  independently. There is a 0.8 probability that the first light is red and a 0.1 probability that the first light is yellow. Also, of the last two lights, each has a probability of 0.7 being green. What is the probability that all 3 will be green when the student passes through them.

11. I am traditionally a morning person, but on the contrast, my Japanese wife experiences problems getting up in the morning. One of the problems is that she experiences difficulties with malfunctioning alarm clocks. Instead of using 1 alarm clock, she decides to use 3. What is the probability that at least 1 alarm clock words correctly if each individual alarm clock has a
98% chance of working correctly?
    
12. (a) If 2 cards are selected from a standard deck of 52 cards without replacement, find the probability that both are diamonds.

(b) If 2 cards are selected from a standard deck of 52 cards without replacement, find the probability that both are the same card.

13. (a) Find the number of ways to arrange 5 people in a straight line.

 (b) Based on your answer from (a), find the probability that the people in a straight line are arranged in age from youngest to oldest.

14. An 4-member FBI investigative team is to be formed from a list of 50 agents not already assigned to a special project.

Out of the 50 agents, how many different possible ways can the team be
formed?

Out of the 50 agents, how many different possible ways can a special investigative team involving 4 members be formed if we would like the first member to be Agent Orange, the second member to be Agent Pink, the third member to be Agent Blue, and the fourth member to be Agent Red?

  
15. (a) How many different 5-digit numbers are there if the first digit is either a 4 or a 7 and if the last digit is even?

(b) Out of all the possible numbers described in (a), what is the probability that the number is 49912?

16. The TishKlean Car Wash© loses $30 on rainy days and gains $120 on days when it does not rain. If the probability of rain is 15%, what is the expected
value of net profit?

17. Consider the following:

 

 

 

-2

 

-0.5

 

-1

 

0

 

0

 

0.2

 

1

 

0.2

 

2

 

0.1

IF the above distribution is a probability distribution, then compute its mean. Otherwise, please state “NOT A PROBABILITY DISTRIBUTION”.

18. According to data from the American Medical Association, 10% of people  are left-handed. In a group of 5 people, find the probability that

 (a) exactly 1 is left-handed. 

(b) at least 2 are left-handed.

  1. at most 4 are right-handed.

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