Problem1 The scores of a reference population on the Wechsler Intelligence Scale

Question

Problem1 The scores of a reference population on the Wechsler Intelligence Scale for Children (WISC) are normally distributed with mean 100 and variance 225. Find the following: a) the probability that a randomly selected child has a score of11 or more b) the probability that a child scores within 2.4 standard deviations from the mean c) the probability a randomly selected child has a score of at least 107, given the score is below 132 d) the score that separates a child from the top 4% of the population from the bottom 96%. Provide the percentile name for this score and the Xa notation. e) the 35th percentile of the scores (also provide the notation for this value) ) the median score Problem2 Busses arrive at a certain stop at 15-minute intervals starting 7:00 am. Suppose a passenger comes to the stop at a time uniformly distributed between 7 and 7:30 am. Find the following: a) the probability that he waits for a bus less than 3 minutes b) the probability that he waits for a bus more than 8 minutes Problem 3 Suppose messages arrive to a computer server according to Poisson process with the rate of 14.7 per hour Find the following: a) the probability that there are no messages in the next four minutes b) the probability that there are no messages in the next three minutes, if there were no messages in the previous 4 minutes c) the probability that it will take between 1 and 4 minutes for the 10th message to arrive after the arrival of the 9th message d) the average time till the next message arrives e) the median of the time till the next message arrives

Explanation / Answer

1)

## a) Answer for a
a <- pnorm(111, mean = 100, sd = 15, lower.tail = FALSE)
a
## b) Answer for b
b<- pnorm(c(100-2.4*15,100+2.4*15), mean = 100, sd = 15, lower.tail = TRUE)
Answer <- b[2]-b[1]
Answer
## c) Answer for c
pXlessthan107 <-pnorm(107,100,15,TRUE)
pxlessthan132 <-pnorm(132,100,15,TRUE)

Answerc<-(pxlessthan132-pXlessthan107)/pxlessthan132
###d) Answer for d
Answerd<-qnorm(0.04,100,15,FALSE)
###e) Answer for e
Answere<-qnorm(0.35,100,15,TRUE)
###answer for f
Answerf<-qnorm(0.5,100,15,TRUE)

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