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Final_Review_1_Solutions

Final_Review_1_Solutions - 0 5 10 15 20 25 30 35(f What...

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0 5 10 15 20 25 30 35 (f) What percent of the students work more than 10 hours a week? 17 + 3 + 3 + 3 + 1 = 27, 27% of the students work more than 10 hours a week. 2. Weights of newborn Golden Retriever puppies follow a normal distribution with mean 12.94 ounces and standard deviation 0.77 ounces. (a) What is the probability that a randomly chosen Golden Retriever puppy is heavier than 14 ounces? Let X represent the weights of Golden Retriever puppies. Then, X N ( μ = 12 . 94 , σ = . 77) P ( X > 14) = P
Z > 14 12 . 94 0 . 77
= P ( Z > 1 . 38) = 1 0 . 9162 = 0 . 0838 (b) What is the probability that a newborn puppy is between 12 and 13 ounces? P (12 < X < 13) = P
Z > 13 12 . 94 0 . 77
P
Z < 12 12 . 94 0 . 77
= P ( Z < 0 . 08) P ( Z < 1 . 22) = 0 . 5319 0 . 1112 = 0 . 4207 (c) The lightest 10% of puppies are considered to be “runts”. What is the cuto ff weight to be considered a “runt”? The Z score for the cuto ff for the lower 10%, or the 10% percentile, is -1.28 as P ( Z < 1 . 28) = 0 . 10 . We use this value to solve for the unknown height cuto ff . 1 . 28 = x 12 . 94 0 . 77 x = 11 . 95 ounces 3. A recent housing survey was conducted to determine the price of a typical home in Topanga, CA. The mean price of a house was roughly $1.3 million with a standard deviation of $280,000. There were no houses listed below $600,000 but a few houses above $3 million. i. Based on this information, which of the following statements is (are) true? (a) Most houses in Topanga cost less than $ 1.3 million. (b) The sampling distribution of average prices of 20 randomly sampled houses is nearly normal. 2
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(c) The sampling distribution of average prices of 20 randomly sampled houses is right skewed. (d) Probability that a randomly chosen house costs more than $1.44 million can be calculated using a normal distribution. (e) Probability that the average price of 49 randomly selected houses is more than $ 1.44 million can be calculated using a normal distribution. ii. Calculate the probability that the average price of 49 randomly selected houses in Topanga is more than $1.44 million. P x > 1 , 440 , 000) = P
z > 1 , 440 , 000 1 , 300 , 000 280 , 000 49
= P ( z > 3 . 50) = 1 0 . 9998 = 0 . 0002 4. As an aid in the establishment of personnel requirements, the director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 64 di ff erent 24-hour periods and determines the number of admissions for each. A 95% confidence interval based on this sample is (18 . 575 , 21 . 025). Based on this information, which of the following statements is (are) false ?
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