MATHEMATICS HIGH SCHOOL

For a standard normal distribution, which of the following expressions must always be equal to 1?A) P(z≤-a)-P(-a≤z≤a)+P(z≥a)
B) P(z≤-a)-P(-a≤z≤a)+P(z≥a)
C) P(z≤-a)+P(-a≤z≤a)-P(z≥a)
D) P(z≤-a)+P(-a≤z≤a)+P(Z≥a)

Answers

Answer 1
Answer: P(z ≤ -a) + P(-a ≤ z ≤ a) + P(z ≥ a) = 1 - P(z ≤ a) + [P(z ≤ a) - P(z ≤ -a)] + 1 - P(z ≤ a) = 2 - 2P(z ≤ a) + P(z ≤ a) - [1 - P(z ≤ a)] = 2 - P(z ≤ a) - 1 + P(z ≤ a) = 1

Therefore, option D is the correct answer.
Answer 2
Answer:

Answer:

D. P(z\le -a)+P(-a\le z\le a)+P(z\ge a)

Step-by-step explanation:

Properties of normal distribution-

  1. The normal curve is symmetrical about the mean (μ).
  2. The mean is at the middle of the graph and it divides the area into two equal halves.
  3. The total area under the curve is equal to 1.

The total area under the curve can be divided into parts like,

  1. area below -a, i.e z\le -a,
  2. area between -a to a, i.e -a\le z\le a
  3. area above a, i.e z\ge a

Therefore, P(z\le -a)+P(-a\le z\le a)+P(z\ge a)=1

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Answers

Step-by-step explanation:

Each term is 9 more than the previous term....the common difference, d = 9

an = a1 + 9(n-1)     where a1 is the first term = 4

  this reduces to:   an = 4 + 9n-9

                                an = 9n - 5

the 30th term is then     a30 = 9(30) - 5 = 265

A basketball player is shooting free throws blindfolded. He shoots in groups of 4 shots. Assume that it is equally likely that he will hit or miss a shot. Design and do a simulation to determine the probability that he will hit at least 75% of his shots within the groups. (Hint: Use coins.)

Answers

Let H represent hit and M represent miss, Then sample space

MMMM, MMMH, MMHM, MHMM, HMMM, MMHH, MHMH, HMMH, MHHM, HMHM, HHMM, MHHH, HMHH, HHMH, HHHM, HHHH

He hit at least 75% in 5 occasions.

Therefore, P(hit at least 75%) = 5/16

Answer:

Use 4 coins. Let heads = hit and tails = miss. Toss each coin and record the results in a table. Coin 1Coin 2Coin3Coin 4Set 1HHHHSet 2HTHHSet 3HHTHSet 4THTTSet 5

Repeat the coin tosses until you have recorded 50 sets of 4 tosses each. b. Count the successful outcomes—those with three or four heads. Coin 1Coin 2Coin3Coin 4SuccessSet 1HHHHxSet 2HTHHxSet 3HHTHxSet 4THTTSet 5

Step-by-step explanation:

Divide 85 into the ratio of 2:3:5

Answers

The actual amount that needs to be divided = 85
The ratio in which the amount needs to be divided = 2:3:5
Let us assume the common ratio to be = x
Then
2x + 3x + 5x = 85
10x = 85
x = 85/10
  = 8.5
Then
The ratio in which the number 85 will be divided = 2 * 8.5:3 * 8.5:5 * 8.5
                                                                             = 17:25.5:42.5
So from the above deduction we can see that the number 85 can be divided in the ratio 17:25.5:42.5

54+(x-4)=x ............

Answers