Magnetic surveying is one technique used by archaeologists to determine anomalies arising from variations in magnetic susceptibility. Unusual changes in magnetic susceptibility might (or might not) indicate an important archaeological discovery. Letxbe a random variable that represents a magnetic susceptibility (MS) reading for a randomly chosen site at an archaeological research location. A random sample of120 sitesgave the readings shown in the table below.

Magnetic Susceptibility Readings,

centimeter-gram-second10⁶(cmg10⁶)CommentMagnetic

SusceptibilityNumber of

ReadingsEstimated

Probability"cool"0x< 10

3636/120 =0.30"neutral"10x< 20

4848/120 =0.40"warm"20x< 30

2424/120 =0.20"very interesting"30x< 40

66/120 =0.05"hot spot"40x

66/120 = 0.05

Suppose a "hot spot" is a site with a reading of 40 or higher.

(a) In a binomial setting, let us call success a "hot spot." Use the table above to findp=P(success) =P(40x)

for a single trial.

(b) Suppose you decide to take readings at random until you get your first "hot spot." Letnbe a random variable representing the trial on which you get your first "hot spot." Use the geometric probability distribution to write out a formula forP(n).

P(n) =

(c) What is the probability that you will need more thansixreadings to find the first "hot spot"? ComputeP(n>6).

(Round your answer to three decimal places.)