Answer:
1/32768
Step-by-step explanation:
I don't know how to explain it to you. I am sorry.
Answer:
a. The percentage of vehicles who pass through this construction zone who are exceeding the posted speed limit =90.82%
b. Percentage of vehicles travel through this construction zone with speeds between 50 mph and 55 mph= 2.28%
Step-by-step explanation:
We have to find
a) P(X>40)= 1- P(x=40)
Using the z statistic
Here
x= 40 mph
u= 44mph
σ= 3 mph
z=(40-44)/3=-1.33
From the z-table -1.67 = 0.9082
a) P(X>40)=
Probability exceeding the speed limit = 0.9082 = 90.82%
b) P(50<X<55)
Now
z1 = (50-44)/3 = 2
z2 = (55-44)/3= 3.67
Area for z>3.59 is almost equal to 1
From the z- table we get
P(55 < X < 60) = P((50-44)/3 < z < (55-44)/3)
= P(2 < z < 3.67)
= P(z<3.67) - P(z<2)
= 1 - 0.9772
= 0.0228
or 2.28%
<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>
Always do the parentheses first. In this case, there are two parentheses, so do the parentheses inside the other parentheses first. After that, it’s just simple addition, subtraction, and multiplication.
(69-9)= 60
(60+23)= 83
83x4= 332
