According to one study, brain weights of men are normally distributed with a mean of 1.20kg and a standard deviation of 0.13kg. Use the data to answer

A weather forecaster predicts that the temperature in Antarctica will decrease ${\displaystyle 8^{\circ }F}$ each hour for the next 6 hours. Write and solve an inequality to determine how many hours it will take for the temperature to drop at least ${\displaystyle {36}^{\circ }F}$

Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station. The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task. ${\displaystyle (1,3),(2,6),(3,12),(4,24)}$
Part A: Is this data modeling an algebraic sequence or a geometric sequence? Explain your answer.
Part B: Use a recursive formula to determine the time she will complete station 5.
Part C: Use an explicit formula to find the time she will complete the 9th station.

A parks and recreation department is constructing a new bike path. The path will be parallel to the railroad tracks shown and pass through the parking area al the point ${\displaystyle (4,5).}$ Write an equation that represents the path.

The article “Modeling Sediment and Water Column Interactions for Hydrophobic Pollutants” (Water Research, 1984: 1169-1174) suggests the uniform distribution on the interval (7.5, 20) as a model for depth (cm) of the bioturbation layer in sediment in a certain region. a. What are the mean and variance of depth? b. What is the cdf of depth? c. What is the probability that observed depth is at most 10? Between 10 and 15? d. What is the probability that the observed depth is within 1 standard deviation of the mean value? Within 2 standard deviations?

In 1985, neither Florida nor Georgia had laws banning open alcohol containers in vehicle passenger compartments. By 1990, Florida had passed such a law, but Georgia had not.
(i) Suppose you can collect random samples of the driving-age population in both states, for 1985 and 1990. Let arrest be a binary variable equal to unity if a person was arrested for drunk driving during the year. Without controlling for any other factors, write down a linear probability model that allows you to test whether the open container law reduced the probability of being arrested for drunk driving. Which coefficient in your model measures the effect of the law?
(ii) Why might you want to control for other factors in the model? What might some of these factors be?
(iii) Now, suppose that you can only collect data for 1985 and 1990 at the county level for the two states. The dependent variable would be the fraction of licensed drivers arrested for drunk driving during the year. How does this data structure differ from the individual-level data described in part (i)? What econometric method would you use?

This exercise requires the use of a graphing calculator or computer programmed to do numerical integration. The normal distribution curve, which models the distributions of data in a wide range of applications, is given by the function
${\displaystyle p\left(x\right)=\frac{1}{\sqrt{2{\pi }^{\sigma }}}e-\frac{{(x-\mu )}^2}{2{\sigma }^2}}$
where $\pi$ = 3,14159265 ... and $\sigma$ and $\mu$ are constants called the standard deviation and the mean, respectively. Its graph (for $\sigma =1$ and $\mu =2)$ is shown in the figure.
With ${\displaystyle \sigma =5}$ and $\mu =0$, approximate ${\displaystyle {\int }_0^{+\mathrm{\infty }}p\left(x\right)dx}$.(Round your answer to four decimal places.)

Find the value and interest earned if $8906.54 is invested for 9 years at $\mathrm{\%}$ compounded
a) semiannually
b) continuosly