(a) Consider a t distribution with 19 degrees of freedom. Compute P(t 1.05). Round your a places. P(t21.05) = 1 (b) Consider at distribution with 18 degrees of freedom. Find the value of c such that P(-c- to at least three decimal places.
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A: here given , for part a) degree of freedom = 14 for part b) degree of freedom = 18
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![Use the ALEKS calculator to solve the following problems.
(a) Consider a **t distribution** with **19 degrees of freedom**. Compute \( P(t \ge 1.05) \). Round your answer to at least three decimal places.
\[ P(t \ge 1.05) = \square \]
(b) Consider a **t distribution** with **18 degrees of freedom**. Find the value of \( c \) such that \( P(-c < t < c) = 0.99 \). Round your answer to at least three decimal places.
\[ c = \square \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf648817-a410-42c0-9aed-d7ed1ec84584%2F62f42b21-1e15-453c-9aa1-e6ebb25e5464%2F0dtalkk_processed.jpeg&w=3840&q=75)
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- SAT scores are normally distributed with mean = 1000 and standard deviation = 200. 15) Take a sample of 30 students. According to the Central Limit Theorem, what is the distribution N(A,B) of the sample mean SAT scores x of the 30 students? Put the value of A in the top box and the value of B in the bottom box. (Round B to 2 decimal places) a. b. 16) Using the distribution you found in #15, if you have a sample of 30 students, find the z-score if the sample mean SAT score ("x-bar") for the 30 students is 972. 17) Find the Table A entry for the z-score you found in # 16. ( 18) Using the previous answers in this section, determine the probability that the mean SAT score of the 30 students is below 972.A. P(t10>1.75), where t10 has a t distribution with 10 degrees of freedomFill in the blanks to complete the following statements. (a) For the shape of the distribution of the sample proportion to be approximately normal, it is required that np(1 -p) 2 (D) Suppose the proportion of a population that has a certain characteristic is 0.3. The mean of the sampling distribution of p from this population is u. = (a) For the shape of the distribution of the sample proportion to be approximately normal, it is required that np(1 - p) 2 (Type an integer or a decimal.)
- Q3(a) Consider a t distribution with 20 degrees of freedom. Compute P(-1.64<t<1.64). Round answer to at least 3 decimal places. P(-1.64<t<1.64)= (b) Consider a t distribution with 27 degrees of freedom. Find the value of c such that P(t is less than or equal to c)=0.05. Round answer to at least 3 decimal places. c=Determine the t-value in each of the cases. i Table of t-Distribution Areas Click the icon to view the table of areas under the t-distribution. (a) Find the t-value such that the area in the right tail is 0.05 with 12 degrees of freedom. 1.782 (Round to three decimal places as needed.) (b) Find the t-value such that the area in the right tail is 0.25 with 5 degrees of freedom. 0.727 (Round to three decimal places as needed.) -Area in (c) Find the t-value such that the area left of the t-value is 0.01 with 26 degrees of freedom. [Hint right tail - 2.479 (Round to three decimal places as needed.) (d) Find the critical t-value that corresponds to 95% confidence. Assume 10 degrees of freedom. Table VI (Round to three decimal places as needed.) t-Distribution Area in Right Tail df 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005 127.321 14.089 636.619 31.599 12.924 8.610 6.869 1 1.376 1.963 3.078 6.314 12.706 4.303 3.182 2.776 2.571 15.894 31.821 63.657 9.925 5.841 4.604…
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