Question

Medical research has shown that 25% of people are gluten-intolerant. Consider a randomly chosen sample of eight people. Let the successful outcome be that a person is gluten-intolerant. Write down each of the following values (0) a (i) n What is the probability that exactly 4 are people in this sample is gluten-intolerant. at most 1 person is gluten-intolerant. State two properties of the normal distribution function. It is known that 20.61% of students in a Mathematics class got a higher mark than Eric. The marks are normally distributed with a mean of 56 points and a standard deviation of 8 points. What is the value of Zcrit? Calculate Eric's mark, to the nearest integer.

Answer 1

The mark of Eric is 63.

7 p = proportion of people are gluten-intolerant -25%=0.25 i). VF rp=1-0.25 = 0.75 102 n= Sample size = 8 The probability that exactly 4 gluten-intoterant =P (x=4) = (3) es are people in the sample 8-4 xo.7 0.25 -0.0865 Probability that at most I pesson is glutena intolerant P(x+1)= 3 (2) 0.25% 0.75² 1 2-4 17 P(x=0) AP (x=1) I 0.1001+ 0.2670 0.3671 Two properties of the normal distribution function is a) np>5 and 6) nq. >5. Let a normal The 2.2. be the mask variable and follow distribution with mean , M = 56 points and standard deviation, 8=8 points, value of By the question , P (272 nit.) = 0.2061 - Plze zerit) = 1.0.2061 >> Plze Zenit) a 0.7939 » Zenit = Ft (0.7937) - Zon't = 0.8193 Again, p(x3m) = 0.2061 => pl zahamso) -... =.0.7937 > 2-56 = f*(0.7937) = 0.8193 => 7 = 62,55 8 2-56 8