We need to reject the null hypothesis; there is sufficient evidence to support the claim that the mean speed is greater than 65 miles / hour.
<h3>What is normal distribution?</h3>'Normal distribution is a continuous probability distribution wherein values lie in a symmetrical fashion mostly situated around the mean.'
According to the given problem,
Since the sample size is fairly large (n > 30), we use normal distribution.
The null hypothesis tested is
Mean speed of all cars ≤ 65 miles/hour. (µ ≤ 65)
The alternative hypothesis is
Mean speed of all cars > 65 miles/hour. (µ > 65)
Significance level = 0.05
The test statistic used is Z = - µ/σ / √ n, where
= 68.4, n = 40, σ = 5.7
Therefore, Z = 68.4 - 65 / 5.7 /√40 = 3.77254177
If the calculated value of test statistic is greater than the critical value at the 0.05 significance level,
Upper critical value = 1.644853627
P-value = P (Z > 3.77254177) = 0.000080796
Hence, we can conclude that we should reject the null hypothesis since there is enough evidence to support the claim that the mean speed is greater than 65 miles / hour.
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Answer:
See below.
Step-by-step explanation:
So we know that a gym membership costs $25 plus $14 each month.
In other words, the one-time cost is $25 and there will be a cost of $14 each month.
We can write this as:
Where f(x) equals the total cost given the number of months x.
For 6 months, the total cost will be:
The first step is to name the equations to make the process of solving them easy.
The second step is to multiply each of the equations by the coefficient of the x term in the other equation. In this case, we will multiply equation (1) by 5 to get equation (3) and then multiply equation (2) by 6 to get equation (4).
The next step is to add equation equation(3) and (4) together to get equation (5) as shown below;
The next step is to take the value of y and substitute it into any of the equations above. For this solution, I pick equation (1). The work done to solve for x is shown below.;
The solution for this system of equations is