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2nd Year Statistics Chapter 1 TestNormal Distribution

30 marks · 40 minutes · 21 questions. Covers: CHAP 10: Normal Distribution .

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2nd Year Statistics Chapter 1 Test

2nd Year · Statistics · Punjab (PTB)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 30Time: 40 minutes

Q1. Multiple choice questions (Attempt all · 10 × 1 = 10)

  1. In a normal distribution , Q1 is equal to:

  2. In a standard normal distribution, Q1 is equal to:

    1. 0.7979

    2. 0.6745

    3. -0.6745

    4. -0.7979

  3. In normal distribution mean, median and mode are:

    1. Not equal

    2. Positive

    3. Equal

    4. None

  4. In a normal distribution, the value of  are respectively:

    1. 0 & 3

    2. 3 & 0

    3. 0 & 1

    4. 1 & 3

  5. The number of parameters of normal distribution is:

    1. One

    2. Two

    3. Three

    4. Four

  6. In a normal distribution  of the area lies between the limits.

  7. The two points containing the middle 68.27% area under a normal curve are:

    1. None

  8. The symmetry of the normal distribution about its mean indicates that:

    1. The distribution is bell shaped

    2. The area under the curve on the both sides of the mean is equal

    3. The two tails extend indefinitely on either sides of the mean

    4. All of these

  9. The maximum ordinate of normal distribution at x=u is:

     

    1. Zero

  10. In a normal distribution, what perecentage of the area is contained with the limits ?

    1. 99.73%

    2. 95.45%

    3. 68.27%

    4. 95%

Q2. Short questions (Attempt any 6 of 8 · 6 × 2 = 12)

  1. The grade-point averages of 300 college freshmen follow approximately a normal distribution with a mean of 2.1 and a standard deviation of 0.8. How many of these freshmen would you expect to have a score between 2.5 and 3.5 inclusive if the point averages are computed to the nearest tenth?

  2. If the random variable Z has the standard normal distribution, find. (i) P(Z>1.96)

  3. If  find. (i) P(|Z| < 3)

  4. If  find. (i) P(|Z| < 1)

  5. If , find a if: (i) P(Z > a) = 0.025

  6. In a normal distribution  and P(25 < X < 55)=0.8662. Find P(20 < X < 60).

  7. Find the probability that 200 tosses of a fair coin will result in (i) between 80 and 120 heads inclusive. (ii) less than 90 heads; and (iii) exactly 100 heads (iv) more than 124 heads.

  8. In a normal distribution, . Find (i) the area above 314 (ii) the two values that contain the middle 75% area (iii) Q1 and Q3.

Q3. Long questions (Attempt any 2 of 3 · 2 × 4 = 8)

  1. Find the value of X which corresponds to a standardized value of -2.05 and 0.86 for the following distribution. (i) 

  2. The continuous random variable X is normally distributed with mean  and standard deviation . Given that P(X < 53)=0.04 and P(X <65) =0.97. Find the inter quartile range of the distribution.

  3. In a standard normal distribution, find: (i) a point that has 97.5% area above it, i.e., z 0.025.