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ira [324]
3 years ago
10

Zoe is comparing two local yoga programs. Yo-Yoga charges a $35 registration fee and $90 a month. Essence Yoga charges a registr

ation fee of $75 and $80 per month. After how many months will the 2 programs be the same?
Mathematics
1 answer:
Harrizon [31]3 years ago
4 0

Answer:

After 4 months

Step-by-step explanation:

The cost at both the programs consists of a "fixed cost" (reg fee)  & "variable cost" ( per month fee).

Let number of months be "x"

<u>Yo-Yoga:</u>

35 fixed

90 per month

So equation would be: 35 + 90x

<u>Essence Yoga:</u>

75 fixed

80 per month

So equation would be: 75 + 80x

To find number of month when cost would be same, we equate both equations and solve for x:

35 + 90x = 75 + 80x

10x = 40

x = 40/10

x = 4

hence, after 4 months, both cost would be same

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3 years ago
A simple random sample of size nequals10 is obtained from a population with muequals68 and sigmaequals15. ​(a) What must be true
valentina_108 [34]

Answer:

(a) The distribution of the sample mean (\bar x) is <em>N</em> (68, 4.74²).

(b) The value of P(\bar X is 0.7642.

(c) The value of P(\bar X\geq 69.1) is 0.3670.

Step-by-step explanation:

A random sample of size <em>n</em> = 10 is selected from a population.

Let the population be made up of the random variable <em>X</em>.

The mean and standard deviation of <em>X</em> are:

\mu=68\\\sigma=15

(a)

According to the Central Limit Theorem if we have a population with mean <em>μ</em> and standard deviation <em>σ</em> and we take appropriately huge random samples (<em>n</em> ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Since the sample selected is not large, i.e. <em>n</em> = 10 < 30, for the distribution of the sample mean will be approximately normally distributed, the population from which the sample is selected must be normally distributed.

Then, the mean of the distribution of the sample mean is given by,

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\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{15}{\sqrt{10}}=4.74

Thus, the distribution of the sample mean (\bar x) is <em>N</em> (68, 4.74²).

(b)

Compute the value of P(\bar X as follows:

P(\bar X

                    =P(Z

*Use a <em>z</em>-table for the probability.

Thus, the value of P(\bar X is 0.7642.

(c)

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Apply continuity correction as follows:

P(\bar X\geq 69.1)=P(\bar X> 69.1+0.5)

                    =P(\bar X>69.6)

                    =P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{69.6-68}{4.74})

                    =P(Z>0.34)\\=1-P(Z

Thus, the value of P(\bar X\geq 69.1) is 0.3670.

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Answer:

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