The 70-year long-term record for weather shows that for New York State, the prec
ID: 2931489 • Letter: T
Question
The 70-year long-term record for weather shows that for New York State, the precipitation amount has a normal distribution. (Give your answers correct to four al precipitation has a mean of 39.27 inches and a d deviation of 4.47 inches. The annual (a) What is the probability that next year the total predipitation for New York State is more than 49.3 inches? (b) What is the probability that next year the total precipitation for New York State is between 41.5 and 48.1 inches? (o) what is the probability that next year the total precipitation for New York State is between 29.1 and 38 inches? (d) what is the probability that next year the total precipitation for New York State is more than 34.7 inches? What is the probability that next year the total precipitation for New York State is less than 44.9 inches? (f) What is the probability that next year the total precipitation for New York State is less than 31 inches? You may need to use the appropriate table in Appendix B to answer this questionExplanation / Answer
from normal distribution: zscore =(X-mean)/std deviaiton
hence
a) P(X>49.3)=1-P(X<49.3)=1-P(Z<2.2438)=1-0.9876 =0.0124
b)P(41.5<X<48.1)=P(0.4989<Z<1.9754)=09759-0.6911=0.2848
c)P(29.1<X<38)=P(-2.2752<X<-0.2841)=0.3882-0.0114 =0.3767
d)P(X>34.7)=1-P(X<34.7)=1-P(Z<-1.0224)=1-0.1533=0.8467
e)P(X<44.9)=P(Z<1.2595)=0.8961
f)P(X<31)=P(Z<-1.8501)=0.0321
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.