Please done all correctly and not with pen and paper

1. [4 marks] The following probability density graph shows the number of moves in 20 chess game. What is the probability that a game took between 25 and 45 moves to Checkmate? mm i2: .- - i z OBI -' 5. its. 15 25 35 45 55 55 75 man-mm 2. [2 marks] Capacitors are electronic components used in computers. televisions, smart phones, and other devices. The following table shows a sample of 30 capacitors taken from a production line, in microfarads (HF). A capacitor is rejected it its value lies more than 2% from a nominal value of IOOyF. What is the probability that a capacitor will be rejected? mm.\" III-\"m \"IE-\"mm \"ml-Elm \"mumm- mm 3. [2 marks] Farmer MacDonald grows soybeans. The table shows the heights of a random sample of 30 plants after several weeks. What is the zscore of a plant with a height of 70 cm? mic-m nun-:1! \"Ii-l1.\" M\" Iii-\"Ili- 4. [3 marks] Farmer MacDonald grows soybeans. Several weeks after planting. she measures the heights of 30 plants at random. The mean of the sample is 59.1 cm with a standard deviation of 6.0? cm. What is the probability that a given plant is either less than 45 cm in height or greater than 75 cm in height? 5. [2 marks] A mark of at least 50 is required to pass a course. The marks this year run from a low of 45 to a high of 83, with a mean of 64 and a standard deviation of 5. The professor would like all students to pass, so he adjusts the marks to achieve a mean of 72 with a standard deviation 015. Is this enough to ensure that all students will pass? 6. [2 marks] A newspaper survey reports that only 23% of the voters in a town favor construction of a new skateboard park. The survey claims an accuracy of 13.2%, 19 times out of 20. How many voters were surveyed? 7. [5 marks] A game involves rolling five dice. The probability of rolling five of the same number, quintuples. on a given roll is 0.08. What is the probability of rolling 10 or more quintuples in 100 rolls? 8. [5 marks] A game costs $5 per play. Six numbers, chosen from O to 99 without repetition. are written on a card and placed in a box. A contestant who can guess the six numbers will win 531000000. Is this a fair prize? Provide calculations to support your