Question

Assume that John's weight naturally fluctuates week-to-week around an average of 80kg with a standard deviation of 1.2 kg (and it follows a normal distribution). If John records his weight on two consecutive weeks, what is the probability that the weight difference (either up or down) is under 2kg?

Answer 1

=80, =1.2

We want to find  P( 78 < X < 82)

Where P( 78 < X < 82) = P(x < 82) - P(x < 78)

find   P(x < 82)

P(x < 82) = P(z < 1.67)

using normal z table we get

P(z < 1.67) = 0.9522

P(x < 82) = 0.9522

ind   P(x < 78)

P(x < 78) = P(z < -1.67)

using normal z table we get

P(z < -1.67) = 0.0478

P(x < 78) = 0.0478

P( 78 < X < 82) = P(x < 82) - P(x < 78)

P( 78 < X < 82) = 0.9522−0.0478

P( 78 < X < 82) =0.9044

Probability of the weight difference is under 2 kg = 0.9044