All categories

3 years ago

Umder what conditions can you use a normal distribution to approximate the binomial distrubution

Mathematics

1 answer:

Shtirlitz [24]3 years ago

6 0

Answer:

See Below

Step-by-step explanation:

A binomial distribution is basically the probability of success of failure of an experiment that is repeated many times.

The parameters are "n" and "p".

Where

n is the number of times the experiment is performed, or the number of trials

p is the probability of success

Note: "q" is the probability of failure, or q = 1 - p

** Binomial Distribution is a discrete distribution

A normal distribution is a continuous distribution that is symmetric about the mean. That means, the data closer to mean occurs more frequently.

At times, we can use normal distribution to approximate a binomial distribution. The conditions can be said as:

" we can approximate a binomial distribution using normal distribution when n is large enough "

How large is large enough?

There isn't a precise answer, but we can take a rule of thumb as

If "n*p" and "n*q" is greater than 10, we can say the sample size, or n, is large enough.

We can approximate when this is less than 10 per say, but the approximation won't be that good. So, the more the value is greater than 10, the better the approximation.

You might be interested in

8x + 7 equals -9 solve for x

Montano1993 [528]

The answer to this equation is
x= (1/4)

8 0

3 years ago

A 9-year-old girl did a science fair experiment in which she tested professional touch therapists to see if they could sense he

Orlov [11]

Answer:

We conclude that the the touch therapists does not use a method equivalent to random guesses.

Yes, the results suggest that touch therapists are effective.

Step-by-step explanation:

We are given that in a 9-year-old girl did a science fair experiment in which she tested professional touch therapists to see if they could sense her energy field.

Among 264264 trials, the touch therapists were correct 105105 times.

Let p = proportion that touch therapists uses a random guess method.

Here, random guess means; p = 50%

So, Null Hypothesis, $H_0$ : p = 50% {means that the touch therapists use a method equivalent to random guesses}

Alternate Hypothesis, $H_A$ : p $\neq$ 50% {means that the touch therapists does not use a method equivalent to random guesses}

The test statistics that would be used here One-sample z proportion statistics;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of touch therapists were correct = $\frac{105}{264}$ = 0.39

n = sample of trials = 264

So, test statistics = $\frac{\frac{105}{264} -0.50}{\sqrt{\frac{\frac{105}{264}(1-\frac{105}{264})}{264} } }$

= -3.395

The value of z test statistics is -3.395.

Now, at 0.05 significance level the z table gives critical value of -1.96 and 1.96 for two-tailed test. Since our test statistics does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the the touch therapists does not use a method equivalent to random guesses.

Yes, the results suggest that touch therapists are effective.

3 0

3 years ago

To rent a certain meeting room, a college charges a reservation fee of $19 and an additional fee of $4 per hour. The chemistry c

prisoha [69]

Answer:

t = 5

Step-by-step explanation: