Question

An experiment yields 100 readings all in the range [20,40]. Construct a histogram with 4 subintervals such that the number of readings in each subinterval is given by:22 readings in [20,25)27 readings in [25,30)29 readings in [30,35)22 readings in [35,40]Let X be a reading drawn at random from the set of 100 readings. Use this histogram to estimate the following probabilities: i) P(X<30) ii)P(24<X<35) iii) P(10<X<34)

Answer 1

Histogram:

Mean & STd dev

Formula Ref:

z = (x - μ) / σ

i) P(X<30) = (30-30.05)/5.31 = -0.0094

P(Z < -0.0094) = 0.4962

ii)P(24<X<35)

P(x < 24) = (24-30.05)/5.31 = -1.14

P(X < 35) = (35-30.05)/5.31 = 0.93

P(-1.14 < z < 0.93) = 0.6967

iii) P(10<X<34)

P(Z < 10) = (10-30.05)/5.31 = -3.78

P(z < 34) = (34-30.05)/5.34 = 0.74

P(-3.78 < z < 0.74) = 0.7703