Question

1. True or False - the following scenario depicts an independent relationship between variables (tree growth and air quality): 20% of trees growing in a particular region are not growing to their expected height. In a particular neighborhood in that region, the Air Quality Index is labeled as “Unhealthy for Sensitive Groups” or worse 30% of the time. 10% of the trees in the region grow in this neighborhood. If you randomly measured the growth of a tree in that neighborhood, then the probability that that tree is not growing to its expected height is 33.33%.

2. Say we have a random sample of n = 15 people who visit a library’s website to browse their catalogue. With p = 0.1 of the population proportion who reserve a book while browsing, what is the probability of selecting exactly 14 users who actually make a reservation in the random sample? Please round to the fourth decimal place.

Please give step by step explanation for the two questions. Thank you!

Answer 1

1)False. Though there is a probability that tree is not growing to its expected height is 33.33%. in this scenario they told that, in a particular neighbourhood in that region, the area is labelled as unhealthy for sensitive groups or worse 30% of the times there is only 10% of the trees grow which is very small. Hence we conclude that, tree growth & air quality are not independent.

2) here, we are given that,

n=15

p=population proportion who reserve book while browsing.

Hence, x= the person who reserves a book

x~B(n,p)

Therefore, probability of exactly 14 users will make a reservation in the random sample is,

P(X=14) & it is given by,

Using R software,

P(X=14)= 1.35*10^-13