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1 year ago

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Use the appropriate normal distribution to approximate the resulting binomial distributions. A convenience store owner claims th

at 55% of the people buying from her store, on a certain day of the week, buy coffee during their visit. A random sample of 35 customers is made. If the store owner's claim is correct, what is the probability that fewer than 24 customers in the sample buy coffee during their visit on that certain day of the week?

1 answer:

Naddika [18.5K]1 year ago

6 0

Answer:

0.9256

Step-by-step explanation:

Given that a convenience store owner claims that 55% of the people buying from her store, on a certain day of the week, buy coffee during their visit

Let X be the number of customers who buy from her store, on a certain day of the week, buy coffee during their visit

X is Binomial (35, 0.55)

since each customer is independent of the other and there are two outcomes.

By approximation to normal we find that both np and nq are >5.

So X can be approximated to normal with mean = np = 19.25

and std dev = $\sqrt{npq} \\=2.943$

Required probability = prob that fewer than 24 customers in the sample buy coffee during their visit on that certain day of the week

= $P(X$ (after effecting continuity correction)

= 0.9256

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Step-by-step explanation:

Previous concepts

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And this coefficient is very near to 1 the maximum possible value, so then we can interpret that the relationship between the entrace exam score and the grade point average are strongly linearly correlated .

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Solve this problem if your smart its my lil brothers

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1/4 of the roses are red, 1/3 of the remainder are yellow and the rest are pink. There are 24 more pink roses than red roses. Ho

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<h3>There are 96 roses altogether</h3>

<em><u>Solution:</u></em>

Let "x" be the number of roses

From given,

<em><u>1/4 of the roses are red</u></em>

$Red\ roses = \frac{1}{4} \times x\\\\Red\ roses = \frac{x}{4}$

<em><u>1/3 of the remainder are yellow</u></em>

$Remaining = x - \frac{x}{4}\\\\Remaining = \frac{3x}{4}$

Therefore,

$Yellow\ roses = \frac{1}{3} \times \frac{3x}{4}\\\\Yellow\ roses = \frac{x}{4}$

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$Remaining = \frac{3x}{4} - \frac{x}{4}\\\\Remaining = \frac{2x}{4}\\\\Remaining = \frac{x}{2}$

Therefore,

$Pink\ Roses = \frac{x}{2}$

There are 24 more pink roses than red roses

Therefore,

Number of pink roses = 24 + red roses

$\frac{x}{2} = 24 + \frac{x}{4}\\\\\frac{x}{2} - \frac{x}{4} = 24\\\\\frac{x}{4} = 24\\\\x = 24 \times 4\\\\x = 96$

Thus there are 96 roses altogether

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