<span>A probability distribution is formed from all possible outcomes of a random process (for a random variable X) and the probability associated with each outcome. Probability distributions may either be discrete (distinct/separate outcomes, such as number of children) or continuous (a continuum of outcomes, such as height). A probability density function is defined such that the likelihood of a value of X between a and b equals the integral (area under the curve) between a and b. This probability is always positive. Further, we know that the area under the curve from negative infinity to positive infinity is one.
The normal probability distribution, one of the fundamental continuous distributions of statistics, is actually a family of distributions (an infinite number of distributions with differing means (ÎĽ) and standard deviations (Ď). Because the normal distribution is a continuous distribution, we can not calculate exact probability for an outcome, but instead we calculate a probability for a range of outcomes (for example the probability that a random variable X is greater than 10).
The normal distribution is symmetric and centered on the mean (same as the median and mode). While the x-axis ranges from negative infinity to positive infinity, nearly all of the X values fall within +/- three standard deviations of the mean (99.7% of values), while ~68% are within +/-1 standard deviation and ~95% are within +/- two standard deviations. This is often called the three sigma rule or the 68-95-99.7 rule. The normal density function is shown below (this formula won’t be on the diagnostic!)</span>
Answer:
x = -6,3,15,-12; y = 11,5,-3,15
Step-by-step explanation:
Domain is the x value, so plugged in the x values into the equation and got the y values or range.
Answer/Step-by-step explanation:
✔️Find AC using Pythagorean Theorem:
AC² = 25.2² - 11.3²
AC² = 507.35
AC = √507.35
AC = 22.5 (nearest tenth)
✔️Find m<A using trigonometric ratio:
Reference angle = A
Opp = 11.3
Hyp = 25.2
Sin(A) = opp/hyp
Sin(A) = 11.3/25.2
A = sin^{-1}(11.3/25.2)
A = 26.6° (nearest tenth)
✔️Find m<B using trigonometric ratio:
Reference angle = B
Adj = 11.3
Hyp = 25.2
Cos(A) = adj/hyp
Cos(A) = 11.3/25.2
A = cos^{-1}(11.3/25.2)
A = 63.4° (nearest tenth)
6 years
A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now. This is an exponential function, An exponential function is given by:
Let x be the number of years and y be the allowance. The initial allowance is $8, this means at x = 0, y = 8
Since it increases by 20% each year, i.e 100% + 20% = 1 + 0.2 = 1.2. This means that b = 1.2
Therefore:
To find the number of years will it take to reach $20 per month, we substitute y = 20 and find x
x = 6 years to the nearest year
5/7
explanation: (5-0)/(7-0) = 5/7
