Answer:
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- <u>a) P(X=1) = 0.302526</u>
- <u>b) P(X=5) = 0.010206</u>
- <u>c) P(X=3) = 0.18522</u>
- <u>d) P(X≤3) = 0.92953</u>
- <u>e) P(X≥5) = 0.010935</u>
- <u>f) P(X≤4) = 0.989065</u>
Explanation:
Binomial experiments are modeled by the formula:
Where
- P(X=x) is the probability of exactly x successes
- p is the probability of one success, which must be the same for every trial, and every trial must be independent of other trial.
- n is the number of trials
- 1 - p is the probability of fail
- there are only two possible outcomes for each trial: success or fail.
<u>a.) P (x=1)</u>
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<u>b.) P (x=5)</u>
<u>c.) P (x=3)</u>
Using the same formula:
<u>d.) P (x less than or equal to 3)</u>
- P(X≤3)= P(X=3) + P(X=2) + P(X=1) + P(X=0)
Also,
- P(X≤3) = 1 - P(X≥4) = 1 - P(X=4) - P(X=5) - P(X=6)
You can use either of those approaches. The result is the same.
Using the second one:
- P(X=4) = 0.059335
- P(X=5) = 0.010206
- P(X=6) = 0.000729
- P(X≤3) = 1 - 0.05935 - 0.010206 - 0.000729 = 0.92953
<u>e.) P(x greather than or equal to 5)</u>
- P(X≥5) = 0.010206 + 0.000729 = 0.010935
<u>f.) P(x less than or equal 4)</u>
- P(X≤4) = 1 - P(X≥5) = 1 - P(X=5) - P(X=6)
- P(X≤4) = 1 - 0.010206 - 0.000729 = 0.989065
Answer:8.385
Step-by-step explanation:
Step 1: multiply both sides by 30 (this sounds crazy, but that's 5 and 6's least common multiple) 1/6(j-1)+4=1/5(3j+1) -> 5(j-1)+120=6(3j+1)
Step 2: Distribute 5(j-1)+120=6(3j+1) -> 5j-5+120=18j+6
Step 3: Combine like terms 5j-5+120=18j+6 -> 5j+115=18j+6
Step 4: Isolate the variable 5j+115=18j+6 -> 109=13j
Step 5: Divide to further isolate 109/13=j= 8.385
Answer:
^G=98°
Step-by-step explanation:
So you know that angle x and angle g summed up together make 180°.
^F+^H+^G= 180°
<=> 53°+45°+^G=180°
<=> ^G= 180°-98°=82°
180°-82°=98°
Answer:
-0.5
Step-by-step explanation:
σM=σ/√N
=9/√36
=9/6
=3/2=1.5
Z=(x-μ)/σ/√N
=(19.5-24)/9/√36
=-4.5/1.5=-3
The probability that the sample mean will be larger than 19.5 = -0.5
P(>19.5)=P(Z>-3)= -0.5