A. zero B. negative C. positive
2 answers:
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Answer:
a) 2¹³
b) 0.0873
c) 0.9983
d) 0.9538
Step-by-step explanation:
a) How many different outcomes are possible?
For every toss, there are two possible outcomes (heads or tails), so if we toss the coin 13 times the total of outcomes possible is 2¹³
b) What is the probability of getting exactly 4 heads?
The definition of probability is an event is: number of favourable events/ number of total events.
When we have two possible outcomes p, q and we repeat the experiment multiple times, we apply the Binomial distribution, in this distribution the probability of getting exactly k successes in n trials is given by
where p represents the probability of success. nCk refers to the combinations of k elements out of n elements.
So we have to know how many different ways we can get exactly 4 heads.
let's name p = probability of getting heads = 0.5
1 -p = probability of getting tails = 0.5
We are going to toss the coin 13 different times and we want to get heads 4 times and tails 9 times.
So, by the Binomial Distribution we would have:
P(X=4) = 13C4 (0.5)⁴(0.5)⁹ = 715 (0.5)¹³ = 0.0873
Thus, the probability of getting exactly 4 heads is 0.0873.
c) What is the probability of getting at least 2 heads?
We are going to use the same binomial distribution but now we need at least to heads, this can be written as <u>1 - (P(X=0) + P(X=1))</u>
P(X=0) + P(X=1) = 13C0 (0.5)⁰(0.5)¹³ + 13C1 (0.5)¹(0.5)¹² = 0.0001220703125 + 0.0015869140625 = 0.001708984375
1 - 0.001708984375 = 0.998291015625
The probability of getting at least 2 heads is 0.9983
d) What is the probability of getting at most 9 heads?
We are going to use the same binomial distribution but now we need at most 9 heads. This can be written as <u>1 - (P(X=10) + P(X = 11) + P(X=12) + P(X=13))</u>
1 - (P(X=10) + P(X = 11) + P(X=12) + P(X=13)) =1 -(13C10(0.5)¹⁰(0.5)³ + 13C11(0.5)¹¹(0.5)²+ 13C12(0.5)¹²(0.5)¹ + 13C13(0.5)¹³(0.5)⁰) = 0.95385742188
The probability of getting at most 9 heads is 0.9538
The complete question is :
What is the total length of all meteors that are 1 6/8 inches? A line plot with the title, length of meteors. The data is a measurement in inches. The line plot goes from two eighths to one and seven eighths, with fourteen tick marks in all. The first tick mark is two eighths and has one data point. The second tick mark is three eighths and has three data points. The third tick mark is four eighths and has two data points. The fourth tick mark is five eighths and has no data points. The fifth tick mark is six eighths and has two data points. The sixth tick mark is seven eighths and has no data points. The seventh tick mark is one and has no data points. The eighth tick mark is one and one eighth and has no data points. The ninth tick mark is one and two eighths and has one data point. The tenth tick mark is one and three-eighths and has two data points. The eleventh tick mark is one and four eighths and has no data points. The twelfth tick mark is one and five-eighths and has no data points. The thirteenth tick mark is one and six eighths and has two data points. The fourteenth tick mark is one and seven eighths and has one data point.
A) three and four-eighths inches
B) three and five-eighths inches
C) four and seven-eighths inches
D) three and seven-eighths inches
Answer:
The total length of all meteors that are 1 6/8 inches is three and four-eighths inches.
Given :
Tick 1 exists 2/8 (1 data point)
Tick 2 exists 3/8 (3 data points)
Tick 3 exists 4/8 (2 data points)
Tick 4 exists 5/8 (no points)
Tick 5 exists 6/8 (2 data points)
Tick 6 exists 7/8 (no data points)
Tick 2 exists 3/8 (3 data points)
....
Tick 13 exists (2 data points)
Therefore, total length of all meteors that exist inches :
Length of meteor =
Number of meteors = 2
Therefore, the correct answer is option A. three and four-eighths inches
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