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After 4 interval of six months, Joe to earn same hourly rate as Blaine
<em><u>Solution:</u></em>
Given that,
Amount earned by Joe = $ 14 per hour
Amount earned by Blaine = $ 18 per hour
Lets assume the number of six month intervals be "x"
<em><u>Joe receives a raise of $1.75 every six months</u></em>
Therefore,
Joe earning: 14 + 1.75(number of six month intervals)
Equation for Joe earning: 14 + 1.75x ------- eqn 1
<em><u>Blaine receives a raise of $0.75 every six months</u></em>
Therefore,
Blaine earning: 18 + 0.75(number of six month intervals)
Equation for Blaine earning: 18 + 0.75x ------------ eqn 2
The number of six-month intervals it will take Joe to earn the same hourly rate as Blaine,
Eqn 1 must be equal to eqn 2
Thus after 4 interval of six months, Joe to earn same hourly rate as Blaine.
Answer:
c) Is not a property (hence (d) is not either)
Step-by-step explanation:
Remember that the chi square distribution with k degrees of freedom has this formula
Where N₁ , N₂m .... are independent random variables with standard normal distribution. Since it is a sum of squares, then the chi square distribution cant take negative values, thus (c) is not true as property. Therefore, (d) cant be true either.
Since the chi square is a sum of squares of a symmetrical random variable, it is skewed to the right (values with big absolute value, either positive or negative, will represent a big weight for the graph that is not compensated with values near 0). This shows that (a) is true
The more degrees of freedom the chi square has, the less skewed to the right it is, up to the point of being almost symmetrical for high values of k. In fact, the Central Limit Theorem states that a chi sqare with n degrees of freedom, with n big, will have a distribution approximate to a Normal distribution, therefore, it is not very skewed for high values of n. As a conclusion, the shape of the distribution changes when the degrees of freedom increase, because the distribution is more symmetrical the higher the degrees of freedom are. Thus, (b) is true.