Please answer all the following math questions and show all the steps and work you did to find the answers.

INTHINKING www.inthinking.co.uk Question 1 The sizes of adult codfish caught in the North Atlantic are normally distributed with a mean of 12 kg and a standard deviation of 2.5 kg. (a) Calculate the probability that a randomly selected codfish is less than 10 kg. (b) (i) Calculate the probability that a randomly selected codfish is greater than 15 kg. (ii) Find the expected number of codfish that are greater than 15 kg in a catch of 2000 codfish. Working ...... (a) ( b ) ( 1 )_ (ii )_ (6 marks) 2 in Thinking www.thinkib.net/mathstudiesINTHINKING www.inthinking.co.uk Question 2 The weights of pandas are normally distributed with a mean of 160 ka and a standard deviation of 15 kg. (a) Show this information on the diagram below. (b) Write down the probability that a randomly selected panda is greater than 160 kg. (c) Write down the probability that a randomly selected panda is less than 130 kg. 'd) The probability that a particular panda is less than x kg is 0.2. Find the value of x. Working ...... (b) (C) (d ) (6 marks) In Thinking www.thinkib.net/mathstudies 3INTHINKING www . inthinking . co . uk Question 3 The number of raisins in a box of Raisin Puffs is normally distributed with a mean of 341 and a standard deviation of 32 (a) Find the probability that a randomly selected box of Raisin Puffs contains between 300 and 400 raisins. (b) Given that Gioia eats 300 boxes of Raisin Puffs in her lifetime, find the expected number of boxes containing more than 375 raisins. The probability there are more than y raisins in a box of Raisin Puffs is 0. 15. (c) Find y. Working ...... (a) ( b ) ( C ) (6 marks) In Thinking www.thinkib.net/mathstudiesINTHINKING www.inthinking.co.uk Question 4 The heights of adult giraffes are normally distributed with a mean of 5.2 m and a standard deviation of 0.45 m. (a) On the diagram below, shade the region representing the probability that a randomly chosen giraffe has a height above 4.3 m. (b) Calculate the probability that a giraffe chosen at random is less than 5 m tall. There are 2500 giraffes in Etosha National Park. (c) Calculate an estimate for the number of giraffes greater than 6 m tall. Working ...... (b) (c) (6 marks) In Thinking www.thinkib.net/mathstudies 5INTHINKING www.inthinking.co.uk Question 5 The IQs of IB students are normally distributed with a mean of 110 and a standard deviation of 15. (a) Write down the probability that a randomly chosen student has an IQ within 2 standard deviations of the mean. (b) Write down the probability that a randomly selected IB student has an IQ greater than 125. (c) Calculate the probability that a randomly selected IB student has an IQ between 100 and 120. A particular province has 1200 students taking the IB. (d) Calculate an estimate for the number of students with an IQ greater than 100. Working ...... (a) ( b ) (c) (d) (6 marks) In Thinking www.thinkib.net/mathstudiesINTHINKING www.inthinking.co.uk Question 6 A factory would like to produce a particular type of part for vehicles such that only 2.5% of parts are greater than 52 mm long and 2.5% of parts are less than 50 mm long. The weights of the parts are normally distributed. (a) Write down the mean required for this part. (b) Write down the standard deviation required for this part. (c) Calculate the probability that a randomly selected part is between 49.5 mm and 51 mm long. The factory would like to produce 100,000 of these parts. Parts greater than 52.5 mm in length will have to be discarded. (d) Calculate the expected number of discarded parts. Working .....- (a) ( b ) (C) (6 marks) (d) @ In Thinking 7 www.thinkib.net/mathstudiesINTHINKING www . inthinking . co . uk Question 7 The waiting times at the Department of Motor Vehicles are normally distributed with a mean of 25 minutes and a standard deviation of 3 minutes. (a) Shade the region representing the probability of a randomly selected person having a waiting time between 19 and 28 minutes. (b) Calculate the probability that a randomly selected person has to wait more than 30 minutes. (c) The probability that a particular person waits more t minutes is 0.1. Find the value of t. Working ...... (b ) (c) (6 marks) In Thinking www.thinklb.net/mathstudies 8INTHINKING www.inthinking.co.uk Question 8 The weights of newborn babies are normally distributed with a mean of about 3.4kg and a standard deviation of 1.2kg. Newborn babies' weights are classified as extremely low, low, normal, and high as shown in the table below. Size Weight (kg) Extremely Low Weight