Question

Use the Poisson Distribution to find the indicated probability. 6) The town of Fastville has been experiencing a mean of 59.4 car accidents per year. Find the probability that on a given day the number of car accidents in Fastville is 3. (Assume 365 days in a year.) rovide an appropriate response. 7) Find the area under the standard normal curve to the right of z -1. 8) For the standard normal curve, find the z-score that corresponds to the first quartile. ovide an appropriate response. Use the Standard Normal Table to find the probability. 9) The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a standard deviation of 15 days. Find the probability of a pregnancy lasting more than 300 days. lve the problem. Round to the nearest tenth unless indicated otherwise. 10) Assume that women have heights that are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. Find the value of the quartile Q3.

Answer 1

6) expected number of accident in 1 day=59.4/365=0.163

hence P(3 accidents on a given day)=P(X=3)=e^-0.163*0.163³/3! =0.0006

7)

P(Z>1)=0.1587

8)

z score = -0.67

9)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	268
std deviation   =σ=	15.0000

hence P(pregnancy last more then 300 days):

probability =

P(X>300)

=

P(Z>2.13)=

1-P(Z<2.13)=

1-0.9834=

0.0166

10)

for Q3 corresponding z score =0.67

therefore value of quantile Q3=mean+z*std deviation =63.6+0.67*2.5=65.3