2. For normal distribution of lifespan X, P(X < A) = P(Z < (A - mean) / standard deviation)
Mean = 15.2 years
Standard deviation = 2.1 years
a) P(X > 14) = 1 - P(X < 14)
= 1 - P(Z < (14 - 15.2)/2.1)
= 1 - P(Z < -0.57)
= 1 - 0.2843
= 0.7157
b) P(X < 13) = P(Z < (13 - 15.2)/2.1)
= P(Z < -1.05)
= 0.1469
c) P(12 < X < 18) = P(X < 18) - P(X < 12)
= P(Z < (18 - 15.2)/2.1) - P(Z < (12 - 15.2)/2.1)
= P(Z < 1.33) - P(Z < -1.52)
= 0.9082 - 0.0643
= 0.8439
d) P(lifetime is not between 14 and 16 years) = P(X < 14) + P(X > 16)
= 0.2843 + 1 - P(X < 16)
= 0.2843 + 1 - P(Z < (16 - 15.2)/2.1)
= 0.2843 + 1 - P(Z < 0.38)
= 0.2843 + 1 - 0.6480
= 0.2843 + 0.3520
= 0.6363
l rt in order for you 2. The lifespan of a new refrigerator is normally distributed...
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 13 years, and standard deviation of 2.5 years. If you randomly purchase one item, what is the probability it will last longer than 20 years? A manufacturer knows that their items have a normally distributed lifespan, with a mean of 5.8 years, and standard deviation of 1.9 years. The 5% of items with the shortest lifespan will last less than how many years?
4. A manufacturer knows that their items have a normally distributed lifespan, with a mean of 14.4 years, and standard deviation of 3.2 years. If you randomly purchase 21 items, what is the probability that their mean life will be longer than 15 years? (Give answer to 4 decimal places.) 5. A particular fruit's weights are normally distributed, with a mean of 704 grams and a standard deviation of 12 grams. If you pick 12 fruit at random, what is...
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 14.9 years, and standard deviation of 2.1 years. If you randomly purchase one item, what is the probability it will last longer than 19 years?
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 13 years, and standard deviation of 4.1 years. If you randomly purchase one item, what is the probability it will last longer than 23 years?
A manufacturer knows that their items have a normally distributed length, with a mean of 18 inches, and standard deviation of 5.7 inches. If one item is chosen at random, what is the probability that it is less than 13 inches long? A manufacturer knows that their items have a normally distributed lifespan, with a mean of 2.7 years, and standard deviation of 0.7 years. If you randomly purchase one item, what is the probability it will last longer than...
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...
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 2.3 years, and standard deviation of 0.6 years. If you randomly purchase one item, what is the probability it will last longer than 4 years?
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 2.9 years, and standard deviation of 0.8 years. If you randomly purchase one item, what is the probability it will last longer than 4 years?
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7.5 years, and standard deviation of 1.8 years. If you randomly purchase one item, what is the probability it will last longer than 12 years?
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.1 years, and standard deviation of 4 years. If you randomly purchase one item, what is the probability it will last longer than 1 years?