P(82 - q < x < 82 + q) = 0.44
P(x < 82 + q) - P(82 - q) = 0.44
P(z < (82 + q - 82)/7.4 - P(z < (82 - q - 82)/7.4) = 0.44
P(z < q/7.4) - P(z < -q/7.4) = 0.44
P(z < q/7.4) - (1 - P(z < q/7.4) = 0.44
P(z < q/7.4) - 1 + P(z < q/7.4) = 0.44
2P(z < q/7.4) - 1 = 0.44
2P(z < q/7.4) = 1.44
P(z < q/7.4) = 0.72
P(z < q/7.4) = P(z < 0.583)
q/7.4 = 0.583
q = 0.583 x 7.4 = 4.31
To solve this problem you must apply the proccedure shown below:
1. You have to r<span>ewrite x=12 in polar form. Then, you have:
12=rCos</span><span>θ
2. Then, you must solve for r, as following:
r=12/Cos</span><span>θ
</span> 3. You have that 1/Cosθ=Sec<span>θ, therefore:
</span> r=12(1/Cos<span>θ)
</span> r=12Sec<span>θ
</span> Therefore, as you can see, the answer is: r=12Secθ<span>
</span>
Answer: We reject the null hypothesis, and we use Normal distribution for the test.
Step-by-step explanation:
Since we have given that
We claim that
Null hypothesis : 
Alternate hypothesis : 
There is 5% level of significance.
So, the test statistic would be
Since alternate hypothesis is left tailed test.
So, p-value = P(z≤-2.31)=0.0401
And the P-value =0.0401 is less than the given level of significance i.e. 5% 0.05.
So, we reject the null hypothesis, and we use Normal distribution for the test.
First align the decimal points and the numbers, then add the extra 0's if needed. Lastly, add and the total answer is 14.225.
