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3 years ago

A true false test with 10 questions is given. Compute the probability of scoring exactly 80% by guessing

Mathematics

1 answer:

Anna35 [415]3 years ago

5 0

Answer: 0.04395

Explanation:

Given: 10 true-false questions.

So, we will have 50% chances (probability = 0.5) of being correct.

Prob( Exactly 80% score) = Prob (exactly 8 answers correct)

As we observe, if X= number of correct answers, then X~ Binomial (n=10, p=0.5)

So, Prob( Exactly 80% score) = Prob (exactly 8 answers correct)

= $\binom{10}{8}\times(1/2)^{8}}\times(1/2)^{2}$

= 0.0439453125

= 0.04395

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Step-by-step explanation:

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3 years ago

−2(25)10x for x=15 URGENT PLS HELP

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Answer:

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Step-by-step explanation:

Given: −2(25)10x

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3 years ago

Suppose the time a child spends waiting at for the bus as a school bus stop is exponentially distributed with mean 7 minutes. De

Gala2k [10]

Answer:

The probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.

Step-by-step explanation:

Let the random variable X represent the time a child spends waiting at for the bus as a school bus stop.

The random variable X is exponentially distributed with mean 7 minutes.

Then the parameter of the distribution is, $\lambda=\frac{1}{\mu}=\frac{1}{7}$ .

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$f_{X}(x)=\lambda\cdot e^{-\lambda x};\ x>0,\ \lambda>0$

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$P(6\leq X\leq 9)=\int\limits^{9}_{6} {\lambda\cdot e^{-\lambda x}} \, dx$

$=\int\limits^{9}_{6} {\frac{1}{7}\cdot e^{-\frac{1}{7} \cdot x}} \, dx \\\\=\frac{1}{7}\cdot \int\limits^{9}_{6} {e^{-\frac{1}{7} \cdot x}} \, dx \\\\=[-e^{-\frac{1}{7} \cdot x}]^{9}_{6}\\\\=e^{-\frac{1}{7} \cdot 6}-e^{-\frac{1}{7} \cdot 9}\\\\=0.424373-0.276453\\\\=0.14792\\\\\approx 0.148$

Thus, the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.

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3 years ago

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