Question

1. Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading less than -0.864°C.

P(Z<−0.864)=

2. Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between -0.495°C and 1.88°C.

P(−0.495<Z<1.88)=P(-0.495<Z<1.88)=

3. A manufacturer knows that their items have a normally distributed lifespan, with a mean of 15 years, and standard deviation of 4.3 years.

If you randomly purchase one item, what is the probability it will last longer than 4 years?

Please answer all the question

Answer 1

1)

P(X<−0.864)= P{Z<((-0.864-0)/1)} = P(z<-0.86) using the z table

= 0.1949 or 19.46%

2)

P(−0.495<X<1.88) = P(X<1.88) - P(X<−0.495)

= P{Z<((1.88-0)/1)} - P{Z<((-0.495-0)/1)}

= P(z<1.88) - P(z<-0.495)

= 0.9699 - 0.3121 = 0.6578 or 65.78%

3)

P(X> 4)= 1 - P(X< 4) = 1 - P{Z<((4-15)/4.3)} =1- P(z<-2.56)

= 1- 0.0052 = 0.9948 or 99.48%