Math

Question Find the probability of Josh scoring par or above on a par-70 course given the provided probability distribution. x70P(x)=0.72\sum_{x \geq 70} P(x) = \boxed{0.72}

Studdy Solution

STEP 1

1. The table lists the discrete probabilities of Josh scoring within certain ranges on a par-70 golf course.
2. "Par or above" refers to Josh scoring 70 or more.
3. The probabilities in the table are mutually exclusive events, meaning they do not overlap and each score range can only occur independently.
4. The sum of the probabilities of all the events listed in the table is 1.

STEP 2

1. Identify the score ranges that correspond to "par or above".
2. Sum the probabilities of these score ranges to find the total probability of scoring "par or above".

STEP 3

Identify the score ranges in the table that correspond to "par or above", which is a score of 70 or higher.

STEP 4

The score ranges that correspond to "par or above" are 707470-74, 757975-79, 808480-84, 858985-89, 909490-94, 959995-99, and 100100 or above.

STEP 5

Sum the probabilities of the identified score ranges to calculate the total probability of Josh scoring "par or above".
P(par or above)=P(7074)+P(7579)+P(8084)+P(8589)+P(9094)+P(9599)+P(100 or above) P(\text{par or above}) = P(70-74) + P(75-79) + P(80-84) + P(85-89) + P(90-94) + P(95-99) + P(100 \text{ or above})

STEP 6

Substitute the probabilities from the table into the equation:
P(par or above)=0.28+0.23+0.09+0.07+0.03+0.03+0.01 P(\text{par or above}) = 0.28 + 0.23 + 0.09 + 0.07 + 0.03 + 0.03 + 0.01

STEP 7

Perform the addition to find the total probability:
P(par or above)=0.28+0.23+0.09+0.07+0.03+0.03+0.01=0.74 P(\text{par or above}) = 0.28 + 0.23 + 0.09 + 0.07 + 0.03 + 0.03 + 0.01 = 0.74
The probability of Josh scoring par or above is 0.740.74.

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