5. (from Q68 P 409) A true-false test consists of 50 questions a. (1 mark) What

Question

5. (from Q68 P 409) A true-false test consists of 50 questions a. (1 mark) What percentage does a student need to get right to convince you that they are not merely guessing? b (2 marks) Use the normal distribution to approximate the probability of getting that score or higher if they are guessing. r believes the distribution of their tips has a model that is slightly skewed to the right with a mean of $9.60 and a standard deviation of $5.40. Estimate the probability that their next 10 diners will tip an average of at least $14.

Explanation / Answer

Question 5

Total test questions = 50

Here Pr(True) = Pr(false) = 0.50 when merely guessing

so if he merely guess than he will expectedly correct 25 answer right.

Lets say k is the number which is solved correctly where we reject the null hypothesis that p 0.50

so,

Pr(x >= k; 50 ; 0.5) < 0.05 (as it is oen tailed as nobody will intentionally solve the questions wrong)

so by solving we get

k = 32 here

(b) Now by normal approximation

standard deviation = sqrt(50 * 0.5 * 0.5) = 3.5355

Pr(X >= 32) = NORM (x > 31.5 ; 25 ; 3.5355)

Z = (31.5 - 25)/3.5355 = 1.8384

Pr(Z > 1.8384) = 1 - 0.967 = 0.0323

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