*Please Provide step by step work* A poll Agency reports that 51% of teenagers a
ID: 3134949 • Letter: #
Question
*Please Provide step by step work*
A poll Agency reports that 51% of teenagers aged 12-17 played video games on their cell phone. A random sample of 151 teenagers is drawn. Use table A.2 if needed to round your answers to 4 decimal places.
1. The mean u p is_____
2. The standard deviation is _______
3. The probability that more than 53% of the teenagers in the sample play video games on their cell phone is_______
4. The the probability that the sample proportion who play video games of their cell phone is between 0.46 and 0.56 is ______
5. The probability that the sample proportion who play the video game on their cell phone is less than 0.57 is _____
6. It (would/ would not) be unusual if the sample proportion hwo play video games on their ell phones was less than 0.44, since the probability is ______
Explanation / Answer
1. The mean u p is__0.51___.
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2. The standard deviation is _______
Here,
n = 151
p = 0.51
Hence,
s = standard deviation = sqrt(p(1-p)/n) = 0.040681284 [ANSWER]
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3. The probability that more than 53% of the teenagers in the sample play video games on their cell phone is_______
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 0.53
u = mean = p = 0.51
s = standard deviation = sqrt(p(1-p)/n) = 0.040681284
Thus,
z = (x - u) / s = 0.491626564
Thus, using a table/technology, the right tailed area of this is
P(z > 0.491626564 ) = 0.31149168 [ANSWER]
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4. The the probability that the sample proportion who play video games of their cell phone is between 0.46 and 0.56 is ______
Here,
n = 151
p = 0.51
We first get the z score for the two values. As z = (x - u) / s, then as
x1 = lower bound = 0.46
x2 = upper bound = 0.56
u = mean = p = 0.51
s = standard deviation = sqrt(p(1-p)/n) = 0.040681284
Thus, the two z scores are
z1 = lower z score = (x1 - u)/s = -1.229066411
z2 = upper z score = (x2 - u) / s = 1.229066411
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.109523454
P(z < z2) = 0.890476546
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.780953092 [ANSWER]
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5. The probability that the sample proportion who play the video game on their cell phone is less than 0.57 is _____
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 0.57
u = mean = p = 0.51
s = standard deviation = sqrt(p(1-p)/n) = 0.040681284
Thus,
z = (x - u) / s = 1.474879693
Thus, using a table/technology, the left tailed area of this is
P(z < 1.474879693 ) = 0.929877555 [ANSWER]
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6. It (would/ would not) be unusual if the sample proportion hwo play video games on their ell phones was less than 0.44, since the probability is ______
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 0.44
u = mean = p = 0.51
s = standard deviation = sqrt(p(1-p)/n) = 0.040681284
Thus,
z = (x - u) / s = -1.720692975
Thus, using a table/technology, the left tailed area of this is
P(z < -1.720692975 ) = 0.042653276
Hence,
It [[WOULD]] be unusual if the sample proportion hwo play video games on their ell phones was less than 0.44, since the probability is __0.042653276____ [which is less than 0.05].
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