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Math  /  Data & Statistics

QuestionP(−1.66<Z<0.66) P(-1.66 < Z < 0.66)

Studdy Solution

STEP 1

1. Z Z is a standard normal random variable.
2. We need to find the probability that Z Z falls between −1.66-1.66 and 0.660.66.

STEP 2

1. Use the standard normal distribution table to find probabilities.
2. Calculate the probability for the range (−1.66<Z<0.66)(-1.66 < Z < 0.66).

STEP 3

Look up the probability for Z<0.66 Z < 0.66 using the standard normal distribution table.
P(Z<0.66) P(Z < 0.66)

STEP 4

According to the standard normal distribution table:
P(Z<0.66)≈0.7454 P(Z < 0.66) \approx 0.7454

STEP 5

Look up the probability for Z<−1.66 Z < -1.66 using the standard normal distribution table.
P(Z<−1.66) P(Z < -1.66)

STEP 6

According to the standard normal distribution table:
P(Z<−1.66)≈0.0485 P(Z < -1.66) \approx 0.0485

STEP 7

Calculate the probability for the range −1.66<Z<0.66-1.66 < Z < 0.66 by subtracting the probability of Z<−1.66 Z < -1.66 from the probability of Z<0.66 Z < 0.66 .
P(−1.66<Z<0.66)=P(Z<0.66)−P(Z<−1.66) P(-1.66 < Z < 0.66) = P(Z < 0.66) - P(Z < -1.66)

STEP 8

Substitute the values obtained from the standard normal distribution table:
P(−1.66<Z<0.66)=0.7454−0.0485=0.6969 P(-1.66 < Z < 0.66) = 0.7454 - 0.0485 = 0.6969
The probability is:
0.6969 \boxed{0.6969}

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