1. A random sample of 16 observations is to be drawn from a normal distribution having mean 11 and standard deviation 3.  Let x denote the sample mean.  Find, correct to three decimal places
2. The probability that x will have a value between 9.2 and 12.2
3. The value of c for which Px <c=0.03

(1)

Given that,

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Just from 13/Page mean “=\mu=11” standard deviation “=\sigma=3” “n=16 n\\\mu_{\bar{x}}=11 n\\\sigma_{\bar{x}}=\sigma / \sqrt n=3 / 4=0.75” (2) “\\ \left.\mathrm{P}(9.2<\bar{x}<12.2)=\mathrm{P}\left[(9.2-11) / 0.75<\left(\bar{x}-\mu_{\bar{x}}\right) / \sigma_{\bar{x}}<(12.2-11) / 0.75\right)\right] n\\=\mathrm{P}(-2.4<Z<1.6) n\\=\mathrm{P}(Z<1.6)-\mathrm{P}(Z<-2.4)” Using z table =0.9452-0.0082 probability =0.9370 (3) To find The value of c for which “P(\bar{x}<c)=0.03” “P(\bar{x}<c)=0.03” Using standard normal table, “\begin{aligned}nn&P(Z<z)=0.03 \\nn&=P(Z<-1.88)=0.03nn\end{aligned}” z = -1.88 Using standard normal z table, Using z-score formula “\begin{aligned}nn&\bar{x}=\mathrm{z} \times \sigma_{\bar{x}}{+} \mu_{\bar{x}} \\nn&\bar{x}=-1.88 \times 0.75+11 \\nn&\bar{x}=9.59nn\end{aligned}” So, the value of c =9.59 # What Will You Get? We provide professional writing services to help you score straight A’s by submitting custom written assignments that mirror your guidelines. #### Premium Quality Get result-oriented writing and never worry about grades anymore. We follow the highest quality standards to make sure that you get perfect assignments. #### Experienced Writers Our writers have experience in dealing with papers of every educational level. You can surely rely on the expertise of our qualified professionals. #### On-Time Delivery Your deadline is our threshold for success and we take it very seriously. We make sure you receive your papers before your predefined time. #### 24/7 Customer Support Someone from our customer support team is always here to respond to your questions. So, hit us up if you have got any ambiguity or concern. #### Complete Confidentiality Sit back and relax while we help you out with writing your papers. We have an ultimate policy for keeping your personal and order-related details a secret. #### Authentic Sources We assure you that your document will be thoroughly checked for plagiarism and grammatical errors as we use highly authentic and licit sources. #### Moneyback Guarantee Still reluctant about placing an order? Our 100% Moneyback Guarantee backs you up on rare occasions where you aren’t satisfied with the writing. #### Order Tracking You don’t have to wait for an update for hours; you can track the progress of your order any time you want. We share the status after each step. #### Areas of Expertise Although you can leverage our expertise for any writing task, we have a knack for creating flawless papers for the following document types. # Trusted Partner of 9650+ Students for Writing From brainstorming your paper's outline to perfecting its grammar, we perform every step carefully to make your paper worthy of A grade. ##### Preferred Writer Hire your preferred writer anytime. Simply specify if you want your preferred expert to write your paper and we’ll make that happen. ##### Grammar Check Report Get an elaborate and authentic grammar check report with your work to have the grammar goodness sealed in your document. ##### One Page Summary You can purchase this feature if you want our writers to sum up your paper in the form of a concise and well-articulated summary. ##### Plagiarism Report You don’t have to worry about plagiarism anymore. Get a plagiarism report to certify the uniqueness of your work. ## Free Features66FREE

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