Answer:
65/100 or 13/20
Step-by-step explanation:
65% = 65/100 and simplify to 13/20
Answer:
92.9997<
<99.5203
Step-by-step explanation:
Using the formula for calculating the confidence interval expressed as:
CI = xbar ± Z * S/√n where;
xbar is the sample mean
Z is the z-score at 90% confidence interval
S is the sample standard deviation
n is the sample size
Given parameters
xbar = 96.52
Z at 90% CI = 1.645
S = 10.70.
n = 25
Required
90% confidence interval for the population mean using the sample data.
Substituting the given parameters into the formula, we will have;
CI = 96.52 ± (1.645 * 10.70/√25)
CI = 96.52 ± (1.645 * 10.70/5)
CI = 96.52 ± (1.645 * 2.14)
CI = 96.52 ± (3.5203)
CI = (96.52-3.5203, 96.52+3.5203)
CI = (92.9997, 99.5203)
<em>Hence a 90% confidence interval for the population mean using this sample data is 92.9997<</em>
<em><99.5203</em>
Answer:
Alecia lives farther from school
Step-by-step explanation:
<em>Georgia</em>
we know that
The distance from the school to her home is 67/100 of a mile
![\frac{67}{100}=0.67\ miles](https://tex.z-dn.net/?f=%5Cfrac%7B67%7D%7B100%7D%3D0.67%5C%20miles)
<em>Alecia</em>
we know that
The distance from the school to her home is
3/10 of a mile plus 4/10 of a mile
so
![\frac{3}{10}+\frac{4}{10}=\frac{7}{10}=0.7\ miles](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B10%7D%2B%5Cfrac%7B4%7D%7B10%7D%3D%5Cfrac%7B7%7D%7B10%7D%3D0.7%5C%20miles)
Compare the distances
![0.7\ miles>0.67\ miles](https://tex.z-dn.net/?f=0.7%5C%20miles%3E0.67%5C%20miles)
therefore
Alecia lives farther from school
Answer: 2718
Step-by-step explanation:
Given: Mean score = 85
Standard deviation = 5
Let x be the score of a random student that follows normal distribution.
Then, the probability that a student scored between 90 and 95 will be
![P(90< x < 95)\\\\=P(\dfrac{90-85}{5}](https://tex.z-dn.net/?f=P%2890%3C%20x%20%3C%2095%29%5C%5C%5C%5C%3DP%28%5Cdfrac%7B90-85%7D%7B5%7D%3C%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%3C%5Cdfrac%7B95-85%7D%7B5%7D%29%5C%5C%5C%5C%3D%20P%281%3C%20z%3C%202%29%5C%20%5C%20%5C%20%5C%20%5C%20%5Bz%3D%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%5D%5C%5C%5C%5C%3DP%28z%3C2%29-P%28z%3C1%29%5C%5C%5C%5C%3D0.9772-0.8413%5C%5C%5C%5C%3D0.1359)
The number of students scored between 90 and 95 = 0.1359 x (Total students)
= 0.1359 (20000)
= 2718
Hence, The number of students scored between 90 and 95 = 2718