Question

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 0.537°C.
P(Z<0.537)=

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 greater than -2.016°C.
P(Z>−2.016)=

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 greater than 1.501°C.
P(Z>1.501)=

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 1.178°C and 2.668°C.
P(1.178<Z<2.668)=

Answer 1

(i) P ( Z<0.537 )=0.7043 (From standard normal Z table)

OR, we can find it using R

>pnorm(0.537,0,1)

[1] 0.7043

(ii) P ( Z>−2.016 )=P ( Z<2.016 )=0.9781

OR, we can find it using R

>pnorm(-2.016,0,1,lower.tail=FALSE)

[1] 0.9781

(iii) P (1.178<Z<2.668 )=0.1156

P (1.178<Z<2.668 )=P ( Z<2.668 )−P (Z<1.178 )

P ( Z<2.668 )=0.9962.

Or , we can find it using R

>pnorm(2.668,0,1)

[1] 0.9962

P ( Z<1.178 )=0.8806

Or , we can find it using R

>pnorm(1.178,0,1)

[1] 0.8806

P (1.178<Z<2.668 )=P ( Z<2.668 )−P (Z<1.178 )

P (1.178<Z<2.668 )= 0.9962 - 0.8806 = 0.1156