4. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. In arandom sample of 900, approximately how many people will have IQs between 85 and 120?​

675 people will have score between 85 and 120 Step-by-step explanation:GivenMean = 100SD = 15If we have to find percentage of score between two values we have to find the z-score for both values and then area under the curve for both valuesz-score is given by:for a value x:[tex]z-score = \frac{x-mean}{SD}[/tex]So,For 85:[tex]z-score = z_1 = \frac{85-mean}{SD}\\ = \frac{85-100}{15}\\=\frac{-15}{15}\\=-1[/tex][tex]z-score = z_2 = \frac{120-mean}{SD}\\ = \frac{120-100}{15}\\=\frac{20}{15}\\=1.3333[/tex]Now we have to find the area under the curve for both values of z-score. z-score tables are used for this purpose.So,For z1 : 0.1587For z2: 0.9082The area between z11 and z2:[tex]z_2-z_1 = 0.9082-0.1587=0.7495[/tex]So the probability of score between 85 and 120 is 0.7495As the sample is of 900 people, the people with scores between 85 and 120 will be:900*0.7495 = 674.55 peopleRounding off to nearest whole number675 people will have score between 85 and 120 Keywords: Probability, SDLearn more about probability at:brainly.com/question/10978510brainly.com/question/11007026#LearnwithBrainly