A quiz consists of two questions. Let X_1 = the time it takes a randomly chosen

Question

A quiz consists of two questions. Let X_1 = the time it takes a randomly chosen student to solve question 1 and X_2 = the time it takes a randomly chosen student to solve question 2. Suppose X_1 and X_2 are independent and both normally distributed; X_1 has a mean of 6 mins and standard deviation of 1.2 mins; X_2 has a mean 7 mins and standard deviation of 1.4 mins. What is the probability that a student can complete the quiz within 15 mins? United States, the distribution of the weight of a newborn infant has a mean of 7.5 pounds and standard deviation 1.25 pounds. (a) Describe the distribution of average weights of samples of 50 newborns drawn from this population. (b) What is the mean and variance of the average weights. (c) What is the 90^th percentile of the distribution of the average weights of samples of 50 newborns? (Thats the value that separates the top 10% average weights from the lower 90% average weights.)

Explanation / Answer

here X=X1+X2

hence mean of X =6+7=13

and std deviation =(1.22+1.42)1/2 =1.844

hence P(X<15)=P(Z<(15-13)/1.844) =P(Z<1.0847)=0.8610

5.4) distribution of samle mean will be approximately normal as sample size is >30 as per central limit theorum

b)with mean =7.5 and

std error of mean =std deviation/(n)1/2 =0.1768

variance=(0.1768)2 =0.03125

c)for 90%, z=1.28155

hence corresponding value =mean +z*std deviation =7.7265

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