PLEASE SOLVE USING PYTHON

1. If IQ scores are normally distributed with a mean of 100 and a standard deviation of 5 , what is the probability that a person selected at random will have an IQ of 110 or greater? 2. The amount of hot chocolate dispensed by a hot chocolate machine is normally distributed with a mean of 16.0oz. and a standard deviation of 2oz. If the cups hold 18.0oz., what is the probability that a selected cup will be overfilled? 3. A company manufactures light bulbs. The average lifetime for these bulbs is 4,000 hours with a standard deviation of 200 hrs. What lifetime should the company promote for these bulbs, whereby only 2% of the bulbs burn out before the claimed lifetime? You may assume that the lives of the bulbs are normally distributed. 4. The average life of a certain type of small motor was estimated to be 10 years with a standard deviation of 2 years. The manufacturer of the motor wants to issue a policy that will replace all motors that fail while under guarantee free of cost. If the company has budget to replace only 3% of all the motors that fail, how long a guarantee (in years) should they offer? You may assume that the lives of the motors are normally distributed. Rubric: Solution to each of the above problem should: - Show proper sketch of the normal PDF highlighting the required area and probability =5 points - Correctly use the appropriate Z - tables (half or full) to compute probabilities or required Z score as the case may be =5 points - Show proper conversion between X and Z score as required by the problem =5 points - Contain proper python code that computes and displays required solutions using the scipy package to compute probabilities or Z scores as the case may be =10 points