dataset_name: high_school_statistics
description: 'The following are multiple choice questions (with answers) about high
  school statistics.


  Q: A new smartwatch is manufactured in one part of a factory, then secured for shipping
  in another, independent part of the factory. The weight of the smartwatch has a
  mean of 62 grams and a standard deviation of 1.0 grams. The weight of the packaging
  (box, user''s guide, bubble wrap, etc.) has a mean of 456 grams and a standard deviation
  of 6 grams. Together, the distribution of the weight of the smartwatch and its packaging
  would have the following mean and standard deviation:

  (A) Mean 518 grams; standard deviation 7.0 grams (B) Mean 518 grams; standard deviation
  3.5 grams (C) Mean 518 grams; standard deviation 6.1 grams (D) Mean 394 grams; standard
  deviation 6.1 grams

  A: Let''s think step by step. Since the weight of the watch and the weight of the
  packaging are independent random variables, the mean and variance of their sum is
  equal to the sum of their individual means and variances. So the mean is 62 + 456
  = 518 grams, and the variances is 1.0^2 + 6.0^2 = 37, leading to a standard deviation
  of 6.1 grams. The answer is (C).


  Q: After a frost warning was issued, the owner of a large orange grove asked his
  workers to spray all his trees with water. The water was supposed to freeze and
  form a protective covering of ice around the orange blossom. Nevertheless, the owner
  suspected that some trees suffered considerable damage due to the frost. To estimate
  the proportion of trees that suffered more than 50 percent damage due to the frost,
  he took a random sample of 100 trees from his grove. What is the response variable
  in this experiment?

  (A) The proportion of trees that suffered more than 50 percent damage due to frost.
  (B) The number of trees affected by the frost. (C) The number of trees sampled from
  the grove. (D) For each sampled tree, whether it suffered more than 50 percent damage
  or at most 50 percent damage.

  A: Let''s think step by step. In this experiment, the response variable is what
  is measured. For each tree, what is measured is whether or not it suffered more
  than 50 percent damage due to the frost. The answer is (D).


  Q: Suppose X and Y are random variables with E(X) = 37, var(X) = 5, E(Y) = 62, and
  var(Y) = 12. What are the expected value and variance of the random variable X +
  Y?

  (A) E(X + Y) = 99, var(X + Y) = 8.5 (B) E(X + Y) = 99, var(X + Y) = 13 (C) E(X +
  Y) = 99, var(X + Y) = 17 (D) There is insufficient information to answer this question.

  A: Let''s think step by step. While means of sums of random variables add (regardless
  of whether the variables are independent) in order to determine the variance of
  a sum of random variables, we need to know not just their individual variances but
  the covariance of the two variables, which is not given in this problem. The answer
  is (D).


  Q: Which of the following sets has the smallest standard deviation? Which has the
  largest?

  I: {1,2,3}

  II: {-10,10}

  III: {100}

  (A) I, II (B) II, III (C) III, I (D) III, II

  A: Let''s think step by step. The variance of distribution I is the expected squared
  deviation from its mean (which is 2), so the variance is 2/3 . The variance of distribution
  II is 10^2 (because both elements are 10 away from the mean of zero). The variance
  of distribution III is 0, since it has a single entry. So distribution III has the
  smallest standard deviation and distribution II has the largest. The answer is (D).


  Q: Which of the following is a correct statement about correlation?

  (A) If the slope of the regression line is exactly 1, then the correlation is exactly
  1. (B) If the correlation is 0, then the slope of the regression line is undefined.
  (C) Switching which variable is called x and which is called y changes the sign
  of the correlation. (D) The correlation r is equal to the slope of the regression
  line when z-scores for the y-variable are plotted against z-scores for the x-variable.

  A: Let''s think step by step. Statement A is false because the slope of the regression
  line being exactly 1 can occur even when the two variables are not perfectly correlated.
  Statement B is false because uncorrelated variables regression lines can have slope
  zero. Statement C is false because correlation is symmetric in the two random variables.
  The answer is (D).'
include: _mmlu_flan_cot_fewshot_template_yaml
task: mmlu_flan_cot_fewshot_high_school_statistics
