1) Which of the following is an example of a discrete random variable? a) Jean’s hair color is blue b) Jean weighs 68 kilograms c) Jean ran 350 meters in 3 minutes d) Jean has 6 bags color 2) Which of the following is NOT a continuous random variable? a) The height of the airplane’s flight b) The number of COVID 19 cases in Zamboanga in the month of November c) The amount of liquid on a container d) The length of time for the check up in the hospital 3) Which of the following statement describe a continuous variable? a) A. The number of students who have not returned the modules b) The average speed travelled by a van in a month c) The number of motorists not wearing helmet d) The number of parents who are very cooperative in the school activity 4) Which of the following is a discrete random variable? a) The time it takes to run a race b) The number of students in a classroom c) The weight of a fruit d) The height of a building 5) Which of the following describes a random variable? a) A fixed value determined before an experiment b) A variable that changes during the experiment c) A numerical outcome of a random process d) A variable that is always discrete 6) Which of the following could be an example of a continuous random variable? a) The number of cars in a parking lot b) The number of goals scored in a soccer match c) The weight of a newborn baby d) The number of books on a shelf 7) The sum of the probabilities of all possible outcomes for a random variable must be: a) Equal to 0 b) Less than 1 c) Greater than 1 d) Equal to 1 8) A bag contains 5 red balls and 3 blue balls. If one ball is drawn at random, what is the probability of drawing a blue ball? a) 1/8 b) 3/8 c) 1/2 d) 5/8 9) Which of the following is NOT a discrete variable? a) The number of non-defective laptops  b) The weight of box delivered by the grab driver last December  c) The number of vehicles owned by Teves’s family  d) The number of coins that match when three coins are tossed at once. 10) If a coin is tossed, what are the possible values of the random variable for the number of tails? a) 0,1,2,3 b) 1,2,3 c) 0,1,2 d) 0,1 11) What would be the probability of picking a face card (i.e. a king, queen, or jack)? a) P(Face) = 12/52 = 3/13 b) P(Face) = 4/52 = 1/13  c) P(Face) = 6/52 = 3/26 d) P(Face) = 8/52 = 2/13 12) What do you call the weighted average of the possible values that a random variable can take? a) Variance of discrete random variable b) Simple Variance  c) Mean of discrete random variable d) Simple Mean 13) Find the variance of the probability distribution below. a) 8.04 b) 8.40 c) 9.05 d) 9.50 14) Find the mean of the probability distribution below. a) 4.5 b) 5.18 c) 5.3 d) 6.10 15) Find the standard deviation of the probability distribution below. a) 2.5 b) 2.85 c) 3.0 d) 3.55 16) The number of boxes of face mask being sold by a pharmacy per day are 5, 6, 7, 8, 9, and 10 along with the probabilities of 0.2, 0.1, 0.1,0.1, 0.2 and 0.3 respectively. Calculate the mean of the discrete random variable.  a) 5.9 b) 7.9 c) 6.9 d) 8.9 17) What measure should you use to determine how far or close the probability of events from the center or the mean?  a) Mean of discrete random variable b) Variance of discrete random variable  c) Simple Variance d) Simple Mean 18) What do you call the weighted average of the possible values that a random variable can take? a) Variance of discrete random variable b) Simple Variance  c) Mean of discrete random variable d) Simple Mean 19) What shape is a normal distribution curve? a) Half curve b) Bell curve c) Round curve d) Square curve 20) What is the formula for the mean (μ) of a discrete random variable? a) ∑xP(x) b) ∑x²P(x) c) ∑P(x) d) ∑x 21) The variance of a discrete random variable measures: a) The average outcome b) The spread of the outcomes around the mean c) The most probable outcome d) The total number of outcomes 22) The standard deviation (σ) of a discrete random variable is defined as: a) The square root of the variance b) The square of the variance c) The sum of probabilities d) The mean divided by the variance 23) Which of the following steps is required to compute the variance of a discrete random variable? a) Square each value of the random variable b) Multiply the squared values by their probabilities c) Subtract the mean squared from the result d) All of the above 24) What is the first step in calculating the mean of a discrete random variable? a) Find the probabilities b) Multiply each value by its probability c) Square each value d) Add all the outcomes 25) What is the standard deviation of a random variable with variance 4? a) 16 b) 8 c) 2 d) None of the above 26) Which of the following correctly calculates the variance of a discrete random variable? a) ∑xP(x) b) ∑(x - μ)P(x) c) ∑(x - μ)² P(x) d) ∑x²P(x) 27) If the z-score is 0, where is the data point located? a) One standard deviation above the mean b) One standard deviation below the mean c) At the mean d) Cannot be determined 28) In a standard normal distribution, the mean is: a) 0 b) 1 c) -1 d) Cannot be determined 29) The total area under a normal distribution curve is: a) 0 b) 1 c) 2 d) Infinity 30) If a data point has a z-score of -2, it is located: a) 2 standard deviations above the mean b) 2 standard deviations below the mean c) At the mean d) Cannot be determined 31) A z-score of 1.5 means the data point is: a) 1.5 standard deviations below the mean b) 1.5 standard deviations above the mean c) At the mean d) None of the above 32) What is the shape of a normal distribution? a) Skewed left b) Skewed right c) Bell-shaped d) Uniform 33) What is the probability of a z-score between -1 and 1 in a standard normal distribution? a) Approximately 68% b) Approximately 95% c) Approximately 99.7% d) None of the above 34) For a standard normal distribution, what is the probability of obtaining a z-score less than -1.96? a) 0.025 b) 0.05 c) 0.975 d) 0.95 35) A z-score of 2.5 corresponds to which cumulative probability? a) 0.9938 b) 0.0062 c) 0.9750 d) 0.5000 36) What is the probability of a z-score greater than 1.64 in a standard normal distribution? a) 0.0505 b) 0.0455 c) 0.0555 d) 0.0605 37) In a standard normal distribution, what is the probability of obtaining a z-score between -2.33 and 2.33? a) 0.9012 b) 0.9556 c) 0.9802 d) 0.9938 38) Which best describes the shaded part of this normal distribution graph? a) All data that is one or higher. b) All data that is one or more standard deviations above the mean. c) All data that is between 1 and 3. d) All data that is above the mean. 39) What is the area under the normal curve? a) 0 b) 1 c) 2 d) 3 40) This data is normally distributed. What percent of the data is in the shaded region? a) 68% b) 95% c) 99.7% d) 50% 41) Find the area when the z-score is above 1.92. a) 0.0274 b) 0.0.329 c) 0.5129 d) 0.9726 42) What is the probability that Z is less than 1.00 in the standard normal distribution? a) 0.3413 b) 0.8413 c) 0.5000 d) 0.1587 43) Find P(Z > 1.32) in the standard normal distribution. a) 0.5000 b) 0.8413 c) 0.1587 d) 0.0934 44) What is the value of P(−1.00 < Z < 1.00) in the standard normal distribution? a) 0.6826 b) 0.5000 c) 0.3413 d) 0.1587 45) What is P(Z >1.28) in the standard normal distribution? a) 0.1003 b) 0.8997 c) 0.8413 d) 0.1587 46) In the standard normal distribution, find P(−1.96 < Z < 1.96). a) 0.8500 b) 0.8413 c) 0.9500 d) 0.9973 47) For the standard normal curve, what is P(Z < −0.84)? a) 0.2000 b) 0.2005 c) 0.5000 d) 0.8413 48) Calculate P(0.25 < Z < 1.75) under the standard normal curve. a) 0.5000 b) 0.3944 c) 0.2266 d) 0.3612 49) Calculate P(-2.25<Z<1.55) under the standard normal curve a) 0.5000 b) 0.3944 c) 0.2266 d) 0.9272 50) For a standard normal distribution, what is P(−2.00<Z<0.50)? a) 0.6915 b) 0.6687 c) 0.7257 d) 0.5793

STATISTICS & PROBALITY 11 MID TERM EXAM

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