The distribution of SAT scores of all college-bound seniors taking the SAT in 2014 was approximately normal with a mean of 14971
497 1497 1497 and standard deviation of 322 322 322 322 . Let X=X= X= X, equals the score of a randomly selected tester from this group. Find P(X<1200)P(X<1200) P(X<1200) P, (, X, is less than, 1200, ).
2 answers:
Given Information:
Mean = μ = 1497
Standard deviation = σ = 322
test value = x = 1200
Required Information:
P(x < 1200) = ?
Answer:
P(x < 1200) = 0.17879
Explanation:
First we will find the z-score
P(x < X) = P(z < (x - μ)/σ)
P(x < 1200) = P(z < (1200 - 1497)/322)
P(x < 1200) = P(z < -0.92)
The z-score corresponding to z < -0.92 from z-table is given by
P(z < -0.92) = 0.17879
Therefore, the probability that SAT the test score will be less than 1200 is 0.17879.
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Answer:
The expected value of playing the game is $0.75.
Step-by-step explanation:
The expected value of a random variable is the weighted average of the random variable.
The formula to compute the expected value of a random variable <em>X</em> is:
The random variable <em>X</em> in this case can be defined as the amount won in playing the game.
The probability distribution of <em>X</em> is as follows:
Number on spinner: 1 2 3 4 5 6
Amount earned (<em>X</em>): $1 $4 $7 $10 -$8.75 -$8.75
Probability: 1/6 1/6 1/6 1/6 1/6 1/6
Compute the expected value of <em>X</em> as follows:
Thus, the expected value of playing the game is $0.75.
Let g be the number of grandchildren, and d be the number of dogs. They both have only one head, so the number of heads is
Grandchildren have 2 legs, while dogs have 4. So, the total number of legs is
From the first equation (the one for the heads) we can derive
Substitute this into the second to get
So, there are 9 dogs and (from the first equation